Ashish Awasthi - Academia.edu (original) (raw)

Papers by Ashish Awasthi

Research paper thumbnail of The global, regional, and national burden of cirrhosis by cause in 195 countries and territories, 1990–2017: a systematic analysis for the Global Burden of Disease Study 2017

The Lancet Gastroenterology & Hepatology

Background Cirrhosis and other chronic liver diseases (collectively referred to as cirrhosis in t... more Background Cirrhosis and other chronic liver diseases (collectively referred to as cirrhosis in this paper) are a major cause of morbidity and mortality globally, although the burden and underlying causes difer across locations and demographic groups. We report on results from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2017 on the burden of cirrhosis and its trends since 1990, by cause, sex, and age, for 195 countries and territories. Methods We used data from vital registrations, vital registration samples, and verbal autopsies to estimate mortality. We modelled prevalence of total, compensated, and decompensated cirrhosis on the basis of hospital and claims data. Disability-adjusted life-years (DALYs) were calculated as the sum of years of life lost due to premature death and years lived with disability. Estimates are presented as numbers and age-standardised or age-speciic rates per 100 000 population, with 95% uncertainty intervals (UIs). All estimates are presented for ive causes of cirrhosis: hepatitis B, hepatitis C, alcohol-related liver disease, non-alcoholic steatohepatitis (NASH), and other causes. We compared mortality, prevalence, and DALY estimates with those expected according to the Socio-demographic Index (SDI) as a proxy for the development status of regions and countries. Findings In 2017, cirrhosis caused more than 1•32 million (95% UI 1•27-1•45) deaths (440 000 [416 000-518 000; 33•3%] in females and 883 000 [838 000-967 000; 66•7%] in males) globally, compared with less than 899 000 (829 000-948 000) deaths in 1990. Deaths due to cirrhosis constituted 2•4% (2•3-2•6) of total deaths globally in 2017 compared with 1•9% (1•8-2•0) in 1990. Despite an increase in the number of deaths, the age-standardised death rate decreased from 21•0 (19•2-22•3) per 100 000 population in 1990 to 16•5 (15•8-18•1) per 100 000 population in 2017. Sub-Saharan Africa had the highest age-standardised death rate among GBD super-regions for all years of the study period (32•2 [25•8-38•6] deaths per 100 000 population in 2017), and the high-income super-region had the lowest (10•1 [9•8-10•5] deaths per 100 000 population in 2017). The age-standardised death rate decreased or remained constant from 1990 to 2017 in all GBD regions except eastern Europe and central Asia, where the age-standardised death rate increased, primarily due to increases in alcohol-related liver disease prevalence. At the national level, the age-standardised death rate of cirrhosis was lowest in Singapore in 2017 (3•7 [3•3-4•0] per 100 000 in 2017) and highest in Egypt in all years since 1990 (103•3 [64•4-133•4] per 100 000 in 2017). There were 10•6 million (10•3-10•9) prevalent cases of decompensated cirrhosis and 112 million (107-119) prevalent cases of compensated cirrhosis globally in 2017. There was a signiicant increase in age-standardised prevalence rate of decompensated cirrhosis between 1990 and 2017. Cirrhosis caused by NASH had a steady age-standardised death rate throughout the study period, whereas the other four causes showed declines in age-standardised death rate. The age-standardised prevalence of compensated and decompensated cirrhosis due to NASH increased more than for any other cause of cirrhosis (by 33•2% for compensated cirrhosis and 54•8% for decompensated cirrhosis) over the study period. From 1990 to 2017, the number of prevalent cases more than doubled for compensated cirrhosis due to NASH and more than tripled for decompensated cirrhosis due to NASH. In 2017, age-standardised death and DALY rates were lower among countries and territories with higher SDI. Interpretation Cirrhosis imposes a substantial health burden on many countries and this burden has increased at the global level since 1990, partly due to population growth and ageing. Although the age-standardised death and DALY rates of cirrhosis decreased from 1990 to 2017, numbers of deaths and DALYs and the proportion of all global deaths due to cirrhosis increased. Despite the availability of efective interventions for the prevention and treatment of hepatitis B and C, they were still the main causes of cirrhosis burden worldwide, particularly in low-income countries. The impact of hepatitis B and C is expected to be attenuated and overtaken by that of NASH in the near future. Costefective interventions are required to continue the prevention and treatment of viral hepatitis, and to achieve early diagnosis and prevention of cirrhosis due to alcohol-related liver disease and NASH. Funding Bill & Melinda Gates Foundation.

Research paper thumbnail of A robust numerical scheme for the simulation of nonlinear convection–diffusion–reaction equation

International Journal for Computational Methods in Engineering Science and Mechanics

Research paper thumbnail of Impact of repeated blood pressure measurement on blood pressure categorization in a population-based study from India

Journal of Human Hypertension

Often a single blood pressure (BP) measurement is used to diagnose and manage hypertension in bus... more Often a single blood pressure (BP) measurement is used to diagnose and manage hypertension in busy clinics. However, repeated BP measurements have been shown to be more representative of the true BP status of the individual. Improper measurement of office BP can lead to inaccurate classification, overestimation of a patient’s true BP, unnecessary treatment, and misinterpretation of the true prevalence of hypertension. There is no consensus among major guidelines on the number of recommended measurements at a single visit or the method of arriving at final clinic BP reading. The participants of the National Family Health Survey (NFHS-4), a nationwide survey conducted in India from 2015 to 2016, were used for the analysis. The prevalence and median difference in systolic blood pressure (SBP) and diastolic blood pressure (DBP) for single as well as combinations of two or more readings were calculated. Cross-tabulation was used to assess classification of individuals based on first BP reading compared with the mean of two or more BP measurements. There was a 63% higher prevalence of hypertension when only the first reading was considered for diagnosis in comparison to the mean of the second and third readings. A decrease of 3.6 mmHg and 2.4 mm Hg in mean SBP and DBP, respectively, was observed when the mean of the second and third readings was compared to the first reading. In those who are identified to have grade 1 or higher categories of hypertension, we recommend three BP measurements, with the mean of the second and third measurements being the clinic BP.

Research paper thumbnail of A systematic literature review of Burgers’ equation with recent advances

Pramana

Even if numerical simulation of the Burgers' equation is well documented in the literatur... more Even if numerical simulation of the Burgers' equation is well documented in the literature, a detailed literature survey indicates that gaps still exist for comparative discussion regarding the physical and mathematical significance of the Burgers' equation. Recently, an increasing interest has been developed within the scientific community, for studying non-linear convective–diffusive partial differential equations partly due to the tremendous improvement in computational capacity. Burgers' equation whose exact solution is well known, is one of the famous non-linear partial differential equations which is suitable for the analysis of various important areas. A brief historical review of not only the mathematical, but also the physical significance of the solution of Burgers' equation is presented, emphasising current research strategies, and the challenges that remain regarding the accuracy, stability and convergence of various schemes are discussed. One of the objectives of this paper is to discuss the recent developments in mathematical modelling of Burgers' equation and thus open doors for improvement. No claim is made that the content of the paper is new. However, it is a sincere effort to outline the physical and mathematical importance of Burgers' equation in the most simplified ways. We throw some light on the plethora of challenges which need to be overcome in the research areas and give motivation for the next breakthrough to take place in a numerical simulation of ordinary/partial differential equations.

Research paper thumbnail of Numerical Treatment of the Modified Burgers’ Equation via Backward Differentiation Formulas of Orders Two and Three

International Journal of Nonlinear Sciences and Numerical Simulation

We present an efficient numerical method for solving the nonlinear modified Burgers’ equation (MB... more We present an efficient numerical method for solving the nonlinear modified Burgers’ equation (MBE) using the multi-step method. The nonlinear MBE is first discretized along the spatial direction alone by using the method of lines technique, and this method converts the MBE to a nonlinear system of ordinary differential equations. Multistep methods are employed to solve the nonlinear system of ordinary differential equations. Applicability of the proposed numerical techniques is established through test examples. Discrete root mean square error norm (L2)(L_{2})(L2) and maximum error norm (Linfty)(L_{\infty})(Linfty) are computed and presented for demonstrating the accuracy of the present numerical method. Numerical experiments supported by figures shows that the proposed numerical scheme shows excellent agreement with exact solution and is superior to some existing numerical methods.

Research paper thumbnail of Global, regional, and national burden of traumatic brain injury and spinal cord injury, 1990–2016: a systematic analysis for the Global Burden of Disease Study 2016

The Lancet Neurology

Background Traumatic brain injury (TBI) and spinal cord injury (SCI) are increasingly recognised ... more Background Traumatic brain injury (TBI) and spinal cord injury (SCI) are increasingly recognised as global health priorities in view of the preventability of most injuries and the complex and expensive medical care they necessitate. We aimed to measure the incidence, prevalence, and years of life lived with disability (YLDs) for TBI and SCI from all causes of injury in every country, to describe how these measures have changed between 1990 and 2016, and to estimate the proportion of TBI and SCI cases caused by different types of injury. Methods We used results from the Global Burden of Diseases, Injuries, and Risk Factors (GBD) Study 2016 to measure the global, regional, and national burden of TBI and SCI by age and sex. We measured the incidence and prevalence of all causes of injury requiring medical care in inpatient and outpatient records, literature studies, and survey data. By use of clinical record data, we estimated the proportion of each cause of injury that required medical care that would result in TBI or SCI being considered as the nature of injury. We used literature studies to establish standardised mortality ratios and applied differential equations to convert incidence to prevalence of long-term disability. Finally, we applied GBD disability weights to calculate YLDs. We used a Bayesian meta-regression tool for epidemiological modelling, used causespecific mortality rates for non-fatal estimation, and adjusted our results for disability experienced with comorbid conditions. We also analysed results on the basis of the Socio-demographic Index, a compound measure of income per capita, education, and fertility. Findings In 2016, there were 27•08 million (95% uncertainty interval [UI] 24•30-30•30 million) new cases of TBI and 0•93 million (0•78-1•16 million) new cases of SCI, with age-standardised incidence rates of 369 (331-412) per 100 000 population for TBI and 13 (11-16) per 100 000 for SCI. In 2016, the number of prevalent cases of TBI was 55•50 million (53•40-57•62 million) and of SCI was 27•04 million (24•98-30•15 million). From 1990 to 2016, the agestandardised prevalence of TBI increased by 8•4% (95% UI 7•7 to 9•2), whereas that of SCI did not change significantly (-0•2% [-2•1 to 2•7]). Age-standardised incidence rates increased by 3•6% (1•8 to 5•5) for TBI, but did not change significantly for SCI (-3•6% [-7•4 to 4•0]). TBI caused 8•1 million (95% UI 6•0-10•4 million) YLDs and SCI caused 9•5 million (6•7-12•4 million) YLDs in 2016, corresponding to age-standardised rates of 111 (82-141) per 100 000 for TBI and 130 (90-170) per 100 000 for SCI. Falls and road injuries were the leading causes of new cases of TBI and SCI in most regions. Interpretation TBI and SCI constitute a considerable portion of the global injury burden and are caused primarily by falls and road injuries. The increase in incidence of TBI over time might continue in view of increases in population density, population ageing, and increasing use of motor vehicles, motorcycles, and bicycles. The number of individuals living with SCI is expected to increase in view of population growth, which is concerning because of the specialised care that people with SCI can require. Our study was limited by data sparsity in some regions, and it will be important to invest greater resources in collection of data for TBI and SCI to improve the accuracy of future assessments. Funding Bill & Melinda Gates Foundation.

Research paper thumbnail of Global Mortality From Firearms, 1990-2016

JAMA, Aug 28, 2018

Understanding global variation in firearm mortality rates could guide prevention policies and int... more Understanding global variation in firearm mortality rates could guide prevention policies and interventions. To estimate mortality due to firearm injury deaths from 1990 to 2016 in 195 countries and territories. This study used deidentified aggregated data including 13 812 location-years of vital registration data to generate estimates of levels and rates of death by age-sex-year-location. The proportion of suicides in which a firearm was the lethal means was combined with an estimate of per capita gun ownership in a revised proxy measure used to evaluate the relationship between availability or access to firearms and firearm injury deaths. Firearm ownership and access. Cause-specific deaths by age, sex, location, and year. Worldwide, it was estimated that 251 000 (95% uncertainty interval [UI], 195 000-276 000) people died from firearm injuries in 2016, with 6 countries (Brazil, United States, Mexico, Colombia, Venezuela, and Guatemala) accounting for 50.5% (95% UI, 42.2%-54.8%) of...

Research paper thumbnail of Level and determinants of precancerous symptoms of cervical cancer in unscreened population of Uttar Pradesh and Rajasthan, India: A pilot study

Clinical Epidemiology and Global Health

Problem considered: Cervical cancer, mainly caused by human papillomavirus infection, is one of t... more Problem considered: Cervical cancer, mainly caused by human papillomavirus infection, is one of the most frequent cancers in women in the developing world including India. The present study attempts to explore the risk factors related to symptoms of cervical cancer. Materials and methods: A total of 1319 females of age groups ranging from 14 years to 85 years were included in the present study and analyzed for symptoms and risk factors for cervical cancer. Results: The prevalence of painful micturition, white discharge per vagina, and pelvic pain in the age group 25–44 years was found to be 22.1%, 21%, and 8%, respectively, and the distribution of symptoms was statistically associated ( p < 0.05) with age. Chances of developing painful micturition were significantly related to age group 45–54 years (AOR = 2.5; 95% C.I.: 1.4–4.5), while the likelihood of developing pelvic pain was significantly related to the females of age groups of below 25 years (AOR = 8.4; 95% C.I.: 1.4–12.1) and 25–34 years (AOR = 7.9; 95% C.I.: 1.7–8.3). Pelvic pain was also independently related to the abnormal age of menarche (≤11 or ≥16 years) (AOR = 3.6; 95% C.I.: 1.6–8.5) concerning the standard age of start. Conclusions: Findings of the study indicate that there is lack of awareness about the key risk factors for cervical cancer among women that pointed out the issue of limited knowledge which may work as an obstacle in health services utilization.

Research paper thumbnail of Factors influencing the consumption of iron and folic acid supplementations in high focus states of India

Clinical Epidemiology and Global Health

Iron deficiency during pregnancy is identified as a serious public health problem in most develop... more Iron deficiency during pregnancy is identified as a serious public health problem in most developing countries including India. In India, the majority of the pregnant women are anemic due to a variety of biological and socioeconomic reasons. The purpose of this study is to assess the factors influencing the consumption of Iron and Folic Acid (IFA) supplementation in high focus states of India. Material and Methods: The present study is based on National Family Health Survey (NFHS-3, 2005-06) data. 11085 Recently delivered women. Variables named religion, place of residence, women's and education, birth order, wealth index, husband's education, husband's occupation, type of caste/tribe, and husband present during antenatal care (ANC) visit were taken as predictors. Women who received at least 90 IFA tablets were considered as outcome variable. Results: Well educated women are four times more likely to adhere recommended dose of iron supplements (OR = 4.21; 95% CI = 3.30-5.36, p < 0.01). Women with birth order below 2 (OR = 2.33; 95% CI = 1.84-2.95, p < 0.01), women whose husbands are present during ANC visits (OR = 2.17; CI = 1.92-2.45, p < 0.01) and women with high socioeconomic status (OR = 2.12; 95% CI = 1.70-2.65, p < 0.01) are more likely to consume at least 90 days' iron supplement. Women who had any mass media exposure had 1.34 times (OR = 1.34; 95% CI = 1.13-1.58, p < 0.01) more chances to intake at least 90 IFA tablets. Conclusions: Higher education and lower birth order infer to more iron consumption among pregnant women.

Research paper thumbnail of Global, Regional, and National Burden of Cardiovascular Diseases for 10 Causes, 1990 to 2015

Journal of the American College of Cardiology, Jan 15, 2017

The burden of cardiovascular diseases (CVDs) remains unclear in many regions of the world. The GB... more The burden of cardiovascular diseases (CVDs) remains unclear in many regions of the world. The GBD (Global Burden of Disease) 2015 study integrated data on disease incidence, prevalence, and mortality to produce consistent, up-to-date estimates for cardiovascular burden. CVD mortality was estimated from vital registration and verbal autopsy data. CVD prevalence was estimated using modeling software and data from health surveys, prospective cohorts, health system administrative data, and registries. Years lived with disability (YLD) were estimated by multiplying prevalence by disability weights. Years of life lost (YLL) were estimated by multiplying age-specific CVD deaths by a reference life expectancy. A sociodemographic index (SDI) was created for each location based on income per capita, educational attainment, and fertility. In 2015, there were an estimated 422.7 million cases of CVD (95% uncertainty interval: 415.53 to 427.87 million cases) and 17.92 million CVD deaths (95% unc...

Research paper thumbnail of Child and Adolescent Health From 1990 to 2015: Findings From the Global Burden of Diseases, Injuries, and Risk Factors 2015 Study

JAMA pediatrics, Jan 3, 2017

Comprehensive and timely monitoring of disease burden in all age groups, including children and a... more Comprehensive and timely monitoring of disease burden in all age groups, including children and adolescents, is essential for improving population health. To quantify and describe levels and trends of mortality and nonfatal health outcomes among children and adolescents from 1990 to 2015 to provide a framework for policy discussion. Cause-specific mortality and nonfatal health outcomes were analyzed for 195 countries and territories by age group, sex, and year from 1990 to 2015 using standardized approaches for data processing and statistical modeling, with subsequent analysis of the findings to describe levels and trends across geography and time among children and adolescents 19 years or younger. A composite indicator of income, education, and fertility was developed (Socio-demographic Index [SDI]) for each geographic unit and year, which evaluates the historical association between SDI and health loss. Global child and adolescent mortality decreased from 14.18 million (95% uncert...

Research paper thumbnail of Burden of Diarrhea in the Eastern Mediterranean Region, 1990-2013: Findings from the Global Burden of Disease Study 2013

The American journal of tropical medicine and hygiene, Jan 7, 2016

Diarrheal diseases (DD) are leading causes of disease burden, death, and disability, especially i... more Diarrheal diseases (DD) are leading causes of disease burden, death, and disability, especially in children in low-income settings. DD can also impact a child's potential livelihood through stunted physical growth, cognitive impairment, and other sequelae. As part of the Global Burden of Disease Study, we estimated DD burden, and the burden attributable to specific risk factors and particular etiologies, in the Eastern Mediterranean Region (EMR) between 1990 and 2013. For both sexes and all ages, we calculated disability-adjusted life years (DALYs), which are the sum of years of life lost and years lived with disability. We estimate that over 125,000 deaths (3.6% of total deaths) were due to DD in the EMR in 2013, with a greater burden of DD in low- and middle-income countries. Diarrhea deaths per 100,000 children under 5 years of age ranged from one (95% uncertainty interval [UI] = 0-1) in Bahrain and Oman to 471 (95% UI = 245-763) in Somalia. The pattern for diarrhea DALYs amo...

Research paper thumbnail of Global, Regional, and National Cancer Incidence, Mortality, Years of Life Lost, Years Lived With Disability, and Disability-Adjusted Life-years for 32 Cancer Groups, 1990 to 2015: A Systematic Analysis for the Global Burden of Disease Study

JAMA oncology, Jan 3, 2016

Cancer is the second leading cause of death worldwide. Current estimates on the burden of cancer ... more Cancer is the second leading cause of death worldwide. Current estimates on the burden of cancer are needed for cancer control planning. To estimate mortality, incidence, years lived with disability (YLDs), years of life lost (YLLs), and disability-adjusted life-years (DALYs) for 32 cancers in 195 countries and territories from 1990 to 2015. Cancer mortality was estimated using vital registration system data, cancer registry incidence data (transformed to mortality estimates using separately estimated mortality to incidence [MI] ratios), and verbal autopsy data. Cancer incidence was calculated by dividing mortality estimates through the modeled MI ratios. To calculate cancer prevalence, MI ratios were used to model survival. To calculate YLDs, prevalence estimates were multiplied by disability weights. The YLLs were estimated by multiplying age-specific cancer deaths by the reference life expectancy. DALYs were estimated as the sum of YLDs and YLLs. A sociodemographic index (SDI) wa...

Research paper thumbnail of Trends, prospects and deprivation index of disability in India: Evidences from census 2001 and 2011

Disability and Health Journal, 2016

Since the dawn of civilization, disabilities have existed in various dimensions of human life. Wo... more Since the dawn of civilization, disabilities have existed in various dimensions of human life. World Health Organization (WHO) defines disability as an umbrella term, covering impairments, activity limitations, and participation restrictions. Globally, approximately 1 billion people have some form of disability, and approximately 20% have significant functioning impairments. This study aims to estimate the level, trends and prospects of disability in 640 districts of India. Data for the present study has been taken from Census of India, 2001 and 2011. A Disability Index was calculated at the district level, and state level indexing was done using the Disability Deprivation Index. The population for the year 2021 was projected using the exponential growth rate method. The Disability Deprivation Index was calculated using child labor, adult unemployment, illiteracy, and the ratio of beggars in the disabled population. The study reveals that the proportion of the disabled population in India was 2.10% in 2001, which increased to 2.21% in 2011. According to the Disability Deprivation Index, Maharashtra was the best-performing state in 2011. There were 4.90 million new cases of disability in India during 2001-11, out of which 1.52 million cases belonged to non-congenital disability. There is a rise in the disabled population in India, which needs special attention. The working status of the disabled is gloomy. The majority of the disabled people are non-working and need adequate rehabilitation measures that would facilitate employment.

Research paper thumbnail of Methods, Systems, and User Interfaces for Graphical Summaries of Network Activities

Research paper thumbnail of Intermediate outcomes of rheumatic mitral stenosis post-balloon mitral valvotomy

Asian cardiovascular & thoracic annals, Jan 28, 2015

Balloon mitral valvotomy is a standard therapeutic modality for managing rheumatic mitral stenosi... more Balloon mitral valvotomy is a standard therapeutic modality for managing rheumatic mitral stenosis. Data on intermediate outcomes of this procedure are limited. Thus we investigated the intermediate outcome after balloon mitral valvotomy performed at a large tertiary center in India. Case records and follow-up data of 2330 patients who underwent valvotomy from June 1999 to December 2005 were retrieved from the hospital information system and analyzed. The median age of the patients was 32 ± 11 years, 1363 were female including 36 who were pregnant, and 379 were in atrial fibrillation. Follow-up ranged from 1 to 14 years (mean 4.5 years, median 4.0 years). The procedural success rate was 93%. Atrial fibrillation, higher functional class, and worse valve morphology were independent predictors of a poor procedural outcome. Patients with sinus rhythm had better event-free survival (10.43 years, 95% confidence interval: 10.1-10.7) compared to those with atrial fibrillation (8.17 years, 9...

Research paper thumbnail of Comparison of mortality trends and patterns between India and Japan

Indian journal of maternal and child health: official publication of Indian Maternal and Child Health Association

Mortality is a sure event in anyone’s life. We can delay it with development of medical sciences ... more Mortality is a sure event in anyone’s life. We can delay it with development of medical sciences but it is unavoidable. Mortality is related to the social and physical conditions as well as living standard of people. There is an empirical relation between development of a society and life expectancy at birth. The present study attempts to compare mortality trend in India and Japan from 1950-2010. India and Japan both have achieved almost equal crude death rate but still India is lagging behind Japan in terms of life expectancy at birth, Infant mortality rate and under five mortality rates which are more refined measures of mortality

Research paper thumbnail of Quasiperiodic Steady-State Analysis of Electronic Circuits by a Spline Basis

Mathematics in Industry, 2010

Multitone Harmonic Balance (HB) is widely used for the simulation of the quasiperiodic steady-sta... more Multitone Harmonic Balance (HB) is widely used for the simulation of the quasiperiodic steady-state of RF circuits. HB is based on a Fourier expansion of the waveforms. Unfortunately, trigonometric polynomials often exhibit poor convergence properties when the signals are not quasi-sinusoidal, which leads to a prohibitive run-time even for small circuits. Moreover, the approximation of sharp transients leads to the well-known Gibbs phenomenon, which cannot be removed by an increase of the number of Fourier coefficients, because convergence is only guaranteed in the L 2 norm. In this paper we present alternative approaches based on cubic or exponential splines for a periodic or quasiperiodic steady state analysis. Furthermore, it is shown below that the amount of coding effort is negligible if an implementation of HB exists.

Research paper thumbnail of A New Approach for Fractal Image Coding: Self-similarity at Smallest Scale

Communications in Computer and Information Science, 2011

Research paper thumbnail of A numerical method based on Crank-Nicolson scheme for Burgers’ equation

Applied Mathematics and Computation, 2006

In this paper, we present a solution based on Crank-Nicolson finite difference method for one-dim... more In this paper, we present a solution based on Crank-Nicolson finite difference method for one-dimensional Burgers' equation. Burgers' equation arises frequently in mathematical modeling of problems in fluid dynamics. Hopf-Cole transformation [E. Hopf, The partial differential equation u t + uu x = mu xx , Commun. Pure Appl. Math. 3 (1950) 201-230, J.D. Cole, On a quasilinear parabolic equation occurring in aerodynamics, Quart. Appl. Math. 9 (1951) 225-236] is used to linearize Burgers' equation, the resulting heat equation is discretized by using Crank-Nicolson finite difference scheme. This method is shown to be unconditionally stable and second order accurate in space and time. Numerical results obtained by the present method have been compared with exact solution for different values of Reynolds' number.

Research paper thumbnail of The global, regional, and national burden of cirrhosis by cause in 195 countries and territories, 1990–2017: a systematic analysis for the Global Burden of Disease Study 2017

The Lancet Gastroenterology & Hepatology

Background Cirrhosis and other chronic liver diseases (collectively referred to as cirrhosis in t... more Background Cirrhosis and other chronic liver diseases (collectively referred to as cirrhosis in this paper) are a major cause of morbidity and mortality globally, although the burden and underlying causes difer across locations and demographic groups. We report on results from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2017 on the burden of cirrhosis and its trends since 1990, by cause, sex, and age, for 195 countries and territories. Methods We used data from vital registrations, vital registration samples, and verbal autopsies to estimate mortality. We modelled prevalence of total, compensated, and decompensated cirrhosis on the basis of hospital and claims data. Disability-adjusted life-years (DALYs) were calculated as the sum of years of life lost due to premature death and years lived with disability. Estimates are presented as numbers and age-standardised or age-speciic rates per 100 000 population, with 95% uncertainty intervals (UIs). All estimates are presented for ive causes of cirrhosis: hepatitis B, hepatitis C, alcohol-related liver disease, non-alcoholic steatohepatitis (NASH), and other causes. We compared mortality, prevalence, and DALY estimates with those expected according to the Socio-demographic Index (SDI) as a proxy for the development status of regions and countries. Findings In 2017, cirrhosis caused more than 1•32 million (95% UI 1•27-1•45) deaths (440 000 [416 000-518 000; 33•3%] in females and 883 000 [838 000-967 000; 66•7%] in males) globally, compared with less than 899 000 (829 000-948 000) deaths in 1990. Deaths due to cirrhosis constituted 2•4% (2•3-2•6) of total deaths globally in 2017 compared with 1•9% (1•8-2•0) in 1990. Despite an increase in the number of deaths, the age-standardised death rate decreased from 21•0 (19•2-22•3) per 100 000 population in 1990 to 16•5 (15•8-18•1) per 100 000 population in 2017. Sub-Saharan Africa had the highest age-standardised death rate among GBD super-regions for all years of the study period (32•2 [25•8-38•6] deaths per 100 000 population in 2017), and the high-income super-region had the lowest (10•1 [9•8-10•5] deaths per 100 000 population in 2017). The age-standardised death rate decreased or remained constant from 1990 to 2017 in all GBD regions except eastern Europe and central Asia, where the age-standardised death rate increased, primarily due to increases in alcohol-related liver disease prevalence. At the national level, the age-standardised death rate of cirrhosis was lowest in Singapore in 2017 (3•7 [3•3-4•0] per 100 000 in 2017) and highest in Egypt in all years since 1990 (103•3 [64•4-133•4] per 100 000 in 2017). There were 10•6 million (10•3-10•9) prevalent cases of decompensated cirrhosis and 112 million (107-119) prevalent cases of compensated cirrhosis globally in 2017. There was a signiicant increase in age-standardised prevalence rate of decompensated cirrhosis between 1990 and 2017. Cirrhosis caused by NASH had a steady age-standardised death rate throughout the study period, whereas the other four causes showed declines in age-standardised death rate. The age-standardised prevalence of compensated and decompensated cirrhosis due to NASH increased more than for any other cause of cirrhosis (by 33•2% for compensated cirrhosis and 54•8% for decompensated cirrhosis) over the study period. From 1990 to 2017, the number of prevalent cases more than doubled for compensated cirrhosis due to NASH and more than tripled for decompensated cirrhosis due to NASH. In 2017, age-standardised death and DALY rates were lower among countries and territories with higher SDI. Interpretation Cirrhosis imposes a substantial health burden on many countries and this burden has increased at the global level since 1990, partly due to population growth and ageing. Although the age-standardised death and DALY rates of cirrhosis decreased from 1990 to 2017, numbers of deaths and DALYs and the proportion of all global deaths due to cirrhosis increased. Despite the availability of efective interventions for the prevention and treatment of hepatitis B and C, they were still the main causes of cirrhosis burden worldwide, particularly in low-income countries. The impact of hepatitis B and C is expected to be attenuated and overtaken by that of NASH in the near future. Costefective interventions are required to continue the prevention and treatment of viral hepatitis, and to achieve early diagnosis and prevention of cirrhosis due to alcohol-related liver disease and NASH. Funding Bill & Melinda Gates Foundation.

Research paper thumbnail of A robust numerical scheme for the simulation of nonlinear convection–diffusion–reaction equation

International Journal for Computational Methods in Engineering Science and Mechanics

Research paper thumbnail of Impact of repeated blood pressure measurement on blood pressure categorization in a population-based study from India

Journal of Human Hypertension

Often a single blood pressure (BP) measurement is used to diagnose and manage hypertension in bus... more Often a single blood pressure (BP) measurement is used to diagnose and manage hypertension in busy clinics. However, repeated BP measurements have been shown to be more representative of the true BP status of the individual. Improper measurement of office BP can lead to inaccurate classification, overestimation of a patient’s true BP, unnecessary treatment, and misinterpretation of the true prevalence of hypertension. There is no consensus among major guidelines on the number of recommended measurements at a single visit or the method of arriving at final clinic BP reading. The participants of the National Family Health Survey (NFHS-4), a nationwide survey conducted in India from 2015 to 2016, were used for the analysis. The prevalence and median difference in systolic blood pressure (SBP) and diastolic blood pressure (DBP) for single as well as combinations of two or more readings were calculated. Cross-tabulation was used to assess classification of individuals based on first BP reading compared with the mean of two or more BP measurements. There was a 63% higher prevalence of hypertension when only the first reading was considered for diagnosis in comparison to the mean of the second and third readings. A decrease of 3.6 mmHg and 2.4 mm Hg in mean SBP and DBP, respectively, was observed when the mean of the second and third readings was compared to the first reading. In those who are identified to have grade 1 or higher categories of hypertension, we recommend three BP measurements, with the mean of the second and third measurements being the clinic BP.

Research paper thumbnail of A systematic literature review of Burgers’ equation with recent advances

Pramana

Even if numerical simulation of the Burgers&#39; equation is well documented in the literatur... more Even if numerical simulation of the Burgers&#39; equation is well documented in the literature, a detailed literature survey indicates that gaps still exist for comparative discussion regarding the physical and mathematical significance of the Burgers&#39; equation. Recently, an increasing interest has been developed within the scientific community, for studying non-linear convective–diffusive partial differential equations partly due to the tremendous improvement in computational capacity. Burgers&#39; equation whose exact solution is well known, is one of the famous non-linear partial differential equations which is suitable for the analysis of various important areas. A brief historical review of not only the mathematical, but also the physical significance of the solution of Burgers&#39; equation is presented, emphasising current research strategies, and the challenges that remain regarding the accuracy, stability and convergence of various schemes are discussed. One of the objectives of this paper is to discuss the recent developments in mathematical modelling of Burgers&#39; equation and thus open doors for improvement. No claim is made that the content of the paper is new. However, it is a sincere effort to outline the physical and mathematical importance of Burgers&#39; equation in the most simplified ways. We throw some light on the plethora of challenges which need to be overcome in the research areas and give motivation for the next breakthrough to take place in a numerical simulation of ordinary/partial differential equations.

Research paper thumbnail of Numerical Treatment of the Modified Burgers’ Equation via Backward Differentiation Formulas of Orders Two and Three

International Journal of Nonlinear Sciences and Numerical Simulation

We present an efficient numerical method for solving the nonlinear modified Burgers’ equation (MB... more We present an efficient numerical method for solving the nonlinear modified Burgers’ equation (MBE) using the multi-step method. The nonlinear MBE is first discretized along the spatial direction alone by using the method of lines technique, and this method converts the MBE to a nonlinear system of ordinary differential equations. Multistep methods are employed to solve the nonlinear system of ordinary differential equations. Applicability of the proposed numerical techniques is established through test examples. Discrete root mean square error norm (L2)(L_{2})(L2) and maximum error norm (Linfty)(L_{\infty})(Linfty) are computed and presented for demonstrating the accuracy of the present numerical method. Numerical experiments supported by figures shows that the proposed numerical scheme shows excellent agreement with exact solution and is superior to some existing numerical methods.

Research paper thumbnail of Global, regional, and national burden of traumatic brain injury and spinal cord injury, 1990–2016: a systematic analysis for the Global Burden of Disease Study 2016

The Lancet Neurology

Background Traumatic brain injury (TBI) and spinal cord injury (SCI) are increasingly recognised ... more Background Traumatic brain injury (TBI) and spinal cord injury (SCI) are increasingly recognised as global health priorities in view of the preventability of most injuries and the complex and expensive medical care they necessitate. We aimed to measure the incidence, prevalence, and years of life lived with disability (YLDs) for TBI and SCI from all causes of injury in every country, to describe how these measures have changed between 1990 and 2016, and to estimate the proportion of TBI and SCI cases caused by different types of injury. Methods We used results from the Global Burden of Diseases, Injuries, and Risk Factors (GBD) Study 2016 to measure the global, regional, and national burden of TBI and SCI by age and sex. We measured the incidence and prevalence of all causes of injury requiring medical care in inpatient and outpatient records, literature studies, and survey data. By use of clinical record data, we estimated the proportion of each cause of injury that required medical care that would result in TBI or SCI being considered as the nature of injury. We used literature studies to establish standardised mortality ratios and applied differential equations to convert incidence to prevalence of long-term disability. Finally, we applied GBD disability weights to calculate YLDs. We used a Bayesian meta-regression tool for epidemiological modelling, used causespecific mortality rates for non-fatal estimation, and adjusted our results for disability experienced with comorbid conditions. We also analysed results on the basis of the Socio-demographic Index, a compound measure of income per capita, education, and fertility. Findings In 2016, there were 27•08 million (95% uncertainty interval [UI] 24•30-30•30 million) new cases of TBI and 0•93 million (0•78-1•16 million) new cases of SCI, with age-standardised incidence rates of 369 (331-412) per 100 000 population for TBI and 13 (11-16) per 100 000 for SCI. In 2016, the number of prevalent cases of TBI was 55•50 million (53•40-57•62 million) and of SCI was 27•04 million (24•98-30•15 million). From 1990 to 2016, the agestandardised prevalence of TBI increased by 8•4% (95% UI 7•7 to 9•2), whereas that of SCI did not change significantly (-0•2% [-2•1 to 2•7]). Age-standardised incidence rates increased by 3•6% (1•8 to 5•5) for TBI, but did not change significantly for SCI (-3•6% [-7•4 to 4•0]). TBI caused 8•1 million (95% UI 6•0-10•4 million) YLDs and SCI caused 9•5 million (6•7-12•4 million) YLDs in 2016, corresponding to age-standardised rates of 111 (82-141) per 100 000 for TBI and 130 (90-170) per 100 000 for SCI. Falls and road injuries were the leading causes of new cases of TBI and SCI in most regions. Interpretation TBI and SCI constitute a considerable portion of the global injury burden and are caused primarily by falls and road injuries. The increase in incidence of TBI over time might continue in view of increases in population density, population ageing, and increasing use of motor vehicles, motorcycles, and bicycles. The number of individuals living with SCI is expected to increase in view of population growth, which is concerning because of the specialised care that people with SCI can require. Our study was limited by data sparsity in some regions, and it will be important to invest greater resources in collection of data for TBI and SCI to improve the accuracy of future assessments. Funding Bill & Melinda Gates Foundation.

Research paper thumbnail of Global Mortality From Firearms, 1990-2016

JAMA, Aug 28, 2018

Understanding global variation in firearm mortality rates could guide prevention policies and int... more Understanding global variation in firearm mortality rates could guide prevention policies and interventions. To estimate mortality due to firearm injury deaths from 1990 to 2016 in 195 countries and territories. This study used deidentified aggregated data including 13 812 location-years of vital registration data to generate estimates of levels and rates of death by age-sex-year-location. The proportion of suicides in which a firearm was the lethal means was combined with an estimate of per capita gun ownership in a revised proxy measure used to evaluate the relationship between availability or access to firearms and firearm injury deaths. Firearm ownership and access. Cause-specific deaths by age, sex, location, and year. Worldwide, it was estimated that 251 000 (95% uncertainty interval [UI], 195 000-276 000) people died from firearm injuries in 2016, with 6 countries (Brazil, United States, Mexico, Colombia, Venezuela, and Guatemala) accounting for 50.5% (95% UI, 42.2%-54.8%) of...

Research paper thumbnail of Level and determinants of precancerous symptoms of cervical cancer in unscreened population of Uttar Pradesh and Rajasthan, India: A pilot study

Clinical Epidemiology and Global Health

Problem considered: Cervical cancer, mainly caused by human papillomavirus infection, is one of t... more Problem considered: Cervical cancer, mainly caused by human papillomavirus infection, is one of the most frequent cancers in women in the developing world including India. The present study attempts to explore the risk factors related to symptoms of cervical cancer. Materials and methods: A total of 1319 females of age groups ranging from 14 years to 85 years were included in the present study and analyzed for symptoms and risk factors for cervical cancer. Results: The prevalence of painful micturition, white discharge per vagina, and pelvic pain in the age group 25–44 years was found to be 22.1%, 21%, and 8%, respectively, and the distribution of symptoms was statistically associated ( p &lt; 0.05) with age. Chances of developing painful micturition were significantly related to age group 45–54 years (AOR = 2.5; 95% C.I.: 1.4–4.5), while the likelihood of developing pelvic pain was significantly related to the females of age groups of below 25 years (AOR = 8.4; 95% C.I.: 1.4–12.1) and 25–34 years (AOR = 7.9; 95% C.I.: 1.7–8.3). Pelvic pain was also independently related to the abnormal age of menarche (≤11 or ≥16 years) (AOR = 3.6; 95% C.I.: 1.6–8.5) concerning the standard age of start. Conclusions: Findings of the study indicate that there is lack of awareness about the key risk factors for cervical cancer among women that pointed out the issue of limited knowledge which may work as an obstacle in health services utilization.

Research paper thumbnail of Factors influencing the consumption of iron and folic acid supplementations in high focus states of India

Clinical Epidemiology and Global Health

Iron deficiency during pregnancy is identified as a serious public health problem in most develop... more Iron deficiency during pregnancy is identified as a serious public health problem in most developing countries including India. In India, the majority of the pregnant women are anemic due to a variety of biological and socioeconomic reasons. The purpose of this study is to assess the factors influencing the consumption of Iron and Folic Acid (IFA) supplementation in high focus states of India. Material and Methods: The present study is based on National Family Health Survey (NFHS-3, 2005-06) data. 11085 Recently delivered women. Variables named religion, place of residence, women's and education, birth order, wealth index, husband's education, husband's occupation, type of caste/tribe, and husband present during antenatal care (ANC) visit were taken as predictors. Women who received at least 90 IFA tablets were considered as outcome variable. Results: Well educated women are four times more likely to adhere recommended dose of iron supplements (OR = 4.21; 95% CI = 3.30-5.36, p < 0.01). Women with birth order below 2 (OR = 2.33; 95% CI = 1.84-2.95, p < 0.01), women whose husbands are present during ANC visits (OR = 2.17; CI = 1.92-2.45, p < 0.01) and women with high socioeconomic status (OR = 2.12; 95% CI = 1.70-2.65, p < 0.01) are more likely to consume at least 90 days' iron supplement. Women who had any mass media exposure had 1.34 times (OR = 1.34; 95% CI = 1.13-1.58, p < 0.01) more chances to intake at least 90 IFA tablets. Conclusions: Higher education and lower birth order infer to more iron consumption among pregnant women.

Research paper thumbnail of Global, Regional, and National Burden of Cardiovascular Diseases for 10 Causes, 1990 to 2015

Journal of the American College of Cardiology, Jan 15, 2017

The burden of cardiovascular diseases (CVDs) remains unclear in many regions of the world. The GB... more The burden of cardiovascular diseases (CVDs) remains unclear in many regions of the world. The GBD (Global Burden of Disease) 2015 study integrated data on disease incidence, prevalence, and mortality to produce consistent, up-to-date estimates for cardiovascular burden. CVD mortality was estimated from vital registration and verbal autopsy data. CVD prevalence was estimated using modeling software and data from health surveys, prospective cohorts, health system administrative data, and registries. Years lived with disability (YLD) were estimated by multiplying prevalence by disability weights. Years of life lost (YLL) were estimated by multiplying age-specific CVD deaths by a reference life expectancy. A sociodemographic index (SDI) was created for each location based on income per capita, educational attainment, and fertility. In 2015, there were an estimated 422.7 million cases of CVD (95% uncertainty interval: 415.53 to 427.87 million cases) and 17.92 million CVD deaths (95% unc...

Research paper thumbnail of Child and Adolescent Health From 1990 to 2015: Findings From the Global Burden of Diseases, Injuries, and Risk Factors 2015 Study

JAMA pediatrics, Jan 3, 2017

Comprehensive and timely monitoring of disease burden in all age groups, including children and a... more Comprehensive and timely monitoring of disease burden in all age groups, including children and adolescents, is essential for improving population health. To quantify and describe levels and trends of mortality and nonfatal health outcomes among children and adolescents from 1990 to 2015 to provide a framework for policy discussion. Cause-specific mortality and nonfatal health outcomes were analyzed for 195 countries and territories by age group, sex, and year from 1990 to 2015 using standardized approaches for data processing and statistical modeling, with subsequent analysis of the findings to describe levels and trends across geography and time among children and adolescents 19 years or younger. A composite indicator of income, education, and fertility was developed (Socio-demographic Index [SDI]) for each geographic unit and year, which evaluates the historical association between SDI and health loss. Global child and adolescent mortality decreased from 14.18 million (95% uncert...

Research paper thumbnail of Burden of Diarrhea in the Eastern Mediterranean Region, 1990-2013: Findings from the Global Burden of Disease Study 2013

The American journal of tropical medicine and hygiene, Jan 7, 2016

Diarrheal diseases (DD) are leading causes of disease burden, death, and disability, especially i... more Diarrheal diseases (DD) are leading causes of disease burden, death, and disability, especially in children in low-income settings. DD can also impact a child's potential livelihood through stunted physical growth, cognitive impairment, and other sequelae. As part of the Global Burden of Disease Study, we estimated DD burden, and the burden attributable to specific risk factors and particular etiologies, in the Eastern Mediterranean Region (EMR) between 1990 and 2013. For both sexes and all ages, we calculated disability-adjusted life years (DALYs), which are the sum of years of life lost and years lived with disability. We estimate that over 125,000 deaths (3.6% of total deaths) were due to DD in the EMR in 2013, with a greater burden of DD in low- and middle-income countries. Diarrhea deaths per 100,000 children under 5 years of age ranged from one (95% uncertainty interval [UI] = 0-1) in Bahrain and Oman to 471 (95% UI = 245-763) in Somalia. The pattern for diarrhea DALYs amo...

Research paper thumbnail of Global, Regional, and National Cancer Incidence, Mortality, Years of Life Lost, Years Lived With Disability, and Disability-Adjusted Life-years for 32 Cancer Groups, 1990 to 2015: A Systematic Analysis for the Global Burden of Disease Study

JAMA oncology, Jan 3, 2016

Cancer is the second leading cause of death worldwide. Current estimates on the burden of cancer ... more Cancer is the second leading cause of death worldwide. Current estimates on the burden of cancer are needed for cancer control planning. To estimate mortality, incidence, years lived with disability (YLDs), years of life lost (YLLs), and disability-adjusted life-years (DALYs) for 32 cancers in 195 countries and territories from 1990 to 2015. Cancer mortality was estimated using vital registration system data, cancer registry incidence data (transformed to mortality estimates using separately estimated mortality to incidence [MI] ratios), and verbal autopsy data. Cancer incidence was calculated by dividing mortality estimates through the modeled MI ratios. To calculate cancer prevalence, MI ratios were used to model survival. To calculate YLDs, prevalence estimates were multiplied by disability weights. The YLLs were estimated by multiplying age-specific cancer deaths by the reference life expectancy. DALYs were estimated as the sum of YLDs and YLLs. A sociodemographic index (SDI) wa...

Research paper thumbnail of Trends, prospects and deprivation index of disability in India: Evidences from census 2001 and 2011

Disability and Health Journal, 2016

Since the dawn of civilization, disabilities have existed in various dimensions of human life. Wo... more Since the dawn of civilization, disabilities have existed in various dimensions of human life. World Health Organization (WHO) defines disability as an umbrella term, covering impairments, activity limitations, and participation restrictions. Globally, approximately 1 billion people have some form of disability, and approximately 20% have significant functioning impairments. This study aims to estimate the level, trends and prospects of disability in 640 districts of India. Data for the present study has been taken from Census of India, 2001 and 2011. A Disability Index was calculated at the district level, and state level indexing was done using the Disability Deprivation Index. The population for the year 2021 was projected using the exponential growth rate method. The Disability Deprivation Index was calculated using child labor, adult unemployment, illiteracy, and the ratio of beggars in the disabled population. The study reveals that the proportion of the disabled population in India was 2.10% in 2001, which increased to 2.21% in 2011. According to the Disability Deprivation Index, Maharashtra was the best-performing state in 2011. There were 4.90 million new cases of disability in India during 2001-11, out of which 1.52 million cases belonged to non-congenital disability. There is a rise in the disabled population in India, which needs special attention. The working status of the disabled is gloomy. The majority of the disabled people are non-working and need adequate rehabilitation measures that would facilitate employment.

Research paper thumbnail of Methods, Systems, and User Interfaces for Graphical Summaries of Network Activities

Research paper thumbnail of Intermediate outcomes of rheumatic mitral stenosis post-balloon mitral valvotomy

Asian cardiovascular & thoracic annals, Jan 28, 2015

Balloon mitral valvotomy is a standard therapeutic modality for managing rheumatic mitral stenosi... more Balloon mitral valvotomy is a standard therapeutic modality for managing rheumatic mitral stenosis. Data on intermediate outcomes of this procedure are limited. Thus we investigated the intermediate outcome after balloon mitral valvotomy performed at a large tertiary center in India. Case records and follow-up data of 2330 patients who underwent valvotomy from June 1999 to December 2005 were retrieved from the hospital information system and analyzed. The median age of the patients was 32 ± 11 years, 1363 were female including 36 who were pregnant, and 379 were in atrial fibrillation. Follow-up ranged from 1 to 14 years (mean 4.5 years, median 4.0 years). The procedural success rate was 93%. Atrial fibrillation, higher functional class, and worse valve morphology were independent predictors of a poor procedural outcome. Patients with sinus rhythm had better event-free survival (10.43 years, 95% confidence interval: 10.1-10.7) compared to those with atrial fibrillation (8.17 years, 9...

Research paper thumbnail of Comparison of mortality trends and patterns between India and Japan

Indian journal of maternal and child health: official publication of Indian Maternal and Child Health Association

Mortality is a sure event in anyone’s life. We can delay it with development of medical sciences ... more Mortality is a sure event in anyone’s life. We can delay it with development of medical sciences but it is unavoidable. Mortality is related to the social and physical conditions as well as living standard of people. There is an empirical relation between development of a society and life expectancy at birth. The present study attempts to compare mortality trend in India and Japan from 1950-2010. India and Japan both have achieved almost equal crude death rate but still India is lagging behind Japan in terms of life expectancy at birth, Infant mortality rate and under five mortality rates which are more refined measures of mortality

Research paper thumbnail of Quasiperiodic Steady-State Analysis of Electronic Circuits by a Spline Basis

Mathematics in Industry, 2010

Multitone Harmonic Balance (HB) is widely used for the simulation of the quasiperiodic steady-sta... more Multitone Harmonic Balance (HB) is widely used for the simulation of the quasiperiodic steady-state of RF circuits. HB is based on a Fourier expansion of the waveforms. Unfortunately, trigonometric polynomials often exhibit poor convergence properties when the signals are not quasi-sinusoidal, which leads to a prohibitive run-time even for small circuits. Moreover, the approximation of sharp transients leads to the well-known Gibbs phenomenon, which cannot be removed by an increase of the number of Fourier coefficients, because convergence is only guaranteed in the L 2 norm. In this paper we present alternative approaches based on cubic or exponential splines for a periodic or quasiperiodic steady state analysis. Furthermore, it is shown below that the amount of coding effort is negligible if an implementation of HB exists.

Research paper thumbnail of A New Approach for Fractal Image Coding: Self-similarity at Smallest Scale

Communications in Computer and Information Science, 2011

Research paper thumbnail of A numerical method based on Crank-Nicolson scheme for Burgers’ equation

Applied Mathematics and Computation, 2006

In this paper, we present a solution based on Crank-Nicolson finite difference method for one-dim... more In this paper, we present a solution based on Crank-Nicolson finite difference method for one-dimensional Burgers' equation. Burgers' equation arises frequently in mathematical modeling of problems in fluid dynamics. Hopf-Cole transformation [E. Hopf, The partial differential equation u t + uu x = mu xx , Commun. Pure Appl. Math. 3 (1950) 201-230, J.D. Cole, On a quasilinear parabolic equation occurring in aerodynamics, Quart. Appl. Math. 9 (1951) 225-236] is used to linearize Burgers' equation, the resulting heat equation is discretized by using Crank-Nicolson finite difference scheme. This method is shown to be unconditionally stable and second order accurate in space and time. Numerical results obtained by the present method have been compared with exact solution for different values of Reynolds' number.