Prabha Rastogi - Academia.edu (original) (raw)

Papers by Prabha Rastogi

International journal of renewable energy exchange, Jul 8, 2023

International Journal of Applied Physics and Mathematics, 2016

International Journal of Mathematics Trends and Technology, Sep 25, 2018

In this paper, we present an analytical solution for different systems of differential equations ... more In this paper, we present an analytical solution for different systems of differential equations by using the differential transformation method. The convergence of this method has been discussed with some examples which are presented to show the ability of the method for linear and non-linear systems of differential equations. We begin by showing how the differential transformation method applies to a non-linear system of differential equations and give two examples to illustrate the sufficiency of the method for linear and non-linear stiff systems of differential equations. The results obtained are in good agreement with the exact solution and Runge-Kutta method. These results show that the technique introduced here is accurate and easy to apply.

International Journal for Scientific Research and Development, 2016

Digital marketing has become a very powerful tool in the recent for manufacturers. It has provide... more Digital marketing has become a very powerful tool in the recent for manufacturers. It has provided a large platform to the customer. Advertising plays an important role in marketing and with the invention of mass media and print media which has become a full-fledged science. Hence digital technology and advertising together brought revolution in the commercial field. It has provided such enormous data that there is no comprehensive method in mathematics to handle marketing process.

International journal of renewable energy exchange, Feb 18, 2023

IOP conference series, May 5, 2020

The requirements for Indian electrical power sector is always a challenging task in terms of pred... more The requirements for Indian electrical power sector is always a challenging task in terms of predication of units of generation of electrical units, load factor (central, state and private) for the power plants, peak demand, peak demand meet and peak demand shortage. The historical data from 1997 to 2018 are used for the analysis. The straight line function and polynomial functions used for the analysis of the data to predict the future. The paper outlines appropriates of the both model in context with the Indian power sector. Further, provide the opportunity to understand the regression coefficient as test condition for the model. The regression coefficients are evaluated for load factor such as 0.9448, 0.9659 and 0.9566 for central, state and private. While regression coefficients for the peak demand and peak demand meet are fairly closer to one. However, the model data values are evaluated and the minimum error in the peak demand is 44% and for peak demand meet is 274 % while maximum deviation in peak demand is 107 and fr peak demand meet is 743%.

International Journal for Scientific Research and Development, 2016

Over the past many centuries river floods have been a matter of great concern throughout India. I... more Over the past many centuries river floods have been a matter of great concern throughout India. India being a country with varied natural habitats is also fortified with several rivers flowing through almost every state. These rivers mostly have their tributaries playing a major role to reach out the remote places that are difficult to reach by the river itself. However, during the time of monsoon or the rainy season these rivers also act as catastrophe originating instruments and thereby resulting in floods. These floods cause heavy destruction causing financial as well as loss of life at many times. One such incident of the river Yamuna during the time of flood is discussed. This paper involves a mathematical approach in the form of constructing graphical network over the flow patterns of the river and its flooded parts. This networks constructed over the network of the river flow will also give rise to the understanding of the cause of the floods and thereby taking proper measures to avoid major losses or minimize losses to an extent

Innovations in Computer Science and Engineering, 2022

In this paper we present zhou's method (DTM) for solving the initial value problems involving... more In this paper we present zhou's method (DTM) for solving the initial value problems involving fifth order ordinary differential equations initial value problems involving fifth order ordinary differential equations we introduce the concept of DTM & applied it to obtain solution of three numerical examples for demonstration. The results are compared with exact solution & DTM method results. There results show that the technique introduced here is accurate & easy to apply. KEYWORDS :-Ordinary differential equitationszhou's Method (DTM), Initial value problem 1.0 Introduction :-The purpose of this paper is to employ the DTM method on examples of ordinary differential equation of fifth order and compared with result obtain by exact solution by using complimentary function & particular integral. In recent years, Bizar J. used for Riccati differential equation(1), Opanuga On numerical solution of systems of ordinary differential equitations by numeriacla analytical method (2), Che...

The data analysis is key parameter in the process optimization. The large data are generated whil... more The data analysis is key parameter in the process optimization. The large data are generated while processes are under consideration. The e-commerce, finance accounting, industrial process planning, industrial production planning, labor planning, inventory planning, etc., are the few names of the sectors and need large data handling for required and/or targeting the final endues and/or services. The different mathematical tools have been used such as AHP, MAHP, WPM, PROMETHEE, VIKOR, Games theory, and curve fitting. However, curve fitting has been used for many industrial applications for the processes planning, inventory planning, labor resources planning, etc. Depending on the data form and ability of researcher, the different curves or lines are used for formulation of the mathematical function. These functions could be straight-line function, second-order polynomial function, third-order polynomial functions, logarithmic, exponential function, etc. This paper discusses the curve...

Over the past many centuries river floods have been a matter of great concern throughout India. I... more Over the past many centuries river floods have been a matter of great concern throughout India. India being a country with varied natural habitats is also fortified with several rivers flowing through almost every state. These rivers mostly have their tributaries playing a major role to reach out the remote places that are difficult to reach by the river itself. However, during the time of monsoon or the rainy season these rivers also act as catastrophe originating instruments and thereby resulting in floods. These floods cause heavy destruction causing financial as well as loss of life at many times. One such incident of the river Yamuna during the time of flood is discussed. This paper involves a mathematical approach in the form of constructing graphical network over the flow patterns of the river and its flooded parts. This networks constructed over the network of the river flow will also give rise to the understanding of the cause of the floods and thereby taking proper measures to avoid major losses or minimize losses to an extent

American Journal of Computational and Applied Mathematics, 2018

In this paper, effective algorithms of finite difference method (FDM) and finite element method (... more In this paper, effective algorithms of finite difference method (FDM) and finite element method (FEM) are designed. The solution of partial differential 2-D Laplace equation in Electrostatics with Dirichlet boundary conditions is evaluated. The electric potential over the complete domain for both methods are calculated. The developed numerical solutions in MATLAB gives results much closer to exact solution when evaluated at different nodes. An error analysis is also presented where the numerical error based on the L2 norm is computed. This error reduces monotonically by reducing the mesh size.

International Journal of Mathematics Trends and Technology

This paper focuses on the use of solving electrostatic one-dimension Poisson differential equatio... more This paper focuses on the use of solving electrostatic one-dimension Poisson differential equation boundary-value problem. Sample problems that introduce the finite element methods are presented here and evaluated with analytical and numerical approaches. These approaches are developed in MATLAB and their solutions are compared and verified. Error analysis is also presented in this paper where the numerical error is compute dusing two different definitions namely the percent error and the error based on the L 2 norm. this numerical error is reduced by increasing in number of elements.

IOP Conference Series: Materials Science and Engineering

International Journal of Mathematics Trends and Technology

International Journal of Mathematics Trends and Technology

International journal of renewable energy exchange, Jul 8, 2023

International Journal of Applied Physics and Mathematics, 2016

International Journal of Mathematics Trends and Technology, Sep 25, 2018

In this paper, we present an analytical solution for different systems of differential equations ... more In this paper, we present an analytical solution for different systems of differential equations by using the differential transformation method. The convergence of this method has been discussed with some examples which are presented to show the ability of the method for linear and non-linear systems of differential equations. We begin by showing how the differential transformation method applies to a non-linear system of differential equations and give two examples to illustrate the sufficiency of the method for linear and non-linear stiff systems of differential equations. The results obtained are in good agreement with the exact solution and Runge-Kutta method. These results show that the technique introduced here is accurate and easy to apply.

International Journal for Scientific Research and Development, 2016

Digital marketing has become a very powerful tool in the recent for manufacturers. It has provide... more Digital marketing has become a very powerful tool in the recent for manufacturers. It has provided a large platform to the customer. Advertising plays an important role in marketing and with the invention of mass media and print media which has become a full-fledged science. Hence digital technology and advertising together brought revolution in the commercial field. It has provided such enormous data that there is no comprehensive method in mathematics to handle marketing process.

International journal of renewable energy exchange, Feb 18, 2023

IOP conference series, May 5, 2020

The requirements for Indian electrical power sector is always a challenging task in terms of pred... more The requirements for Indian electrical power sector is always a challenging task in terms of predication of units of generation of electrical units, load factor (central, state and private) for the power plants, peak demand, peak demand meet and peak demand shortage. The historical data from 1997 to 2018 are used for the analysis. The straight line function and polynomial functions used for the analysis of the data to predict the future. The paper outlines appropriates of the both model in context with the Indian power sector. Further, provide the opportunity to understand the regression coefficient as test condition for the model. The regression coefficients are evaluated for load factor such as 0.9448, 0.9659 and 0.9566 for central, state and private. While regression coefficients for the peak demand and peak demand meet are fairly closer to one. However, the model data values are evaluated and the minimum error in the peak demand is 44% and for peak demand meet is 274 % while maximum deviation in peak demand is 107 and fr peak demand meet is 743%.

International Journal for Scientific Research and Development, 2016

Over the past many centuries river floods have been a matter of great concern throughout India. I... more Over the past many centuries river floods have been a matter of great concern throughout India. India being a country with varied natural habitats is also fortified with several rivers flowing through almost every state. These rivers mostly have their tributaries playing a major role to reach out the remote places that are difficult to reach by the river itself. However, during the time of monsoon or the rainy season these rivers also act as catastrophe originating instruments and thereby resulting in floods. These floods cause heavy destruction causing financial as well as loss of life at many times. One such incident of the river Yamuna during the time of flood is discussed. This paper involves a mathematical approach in the form of constructing graphical network over the flow patterns of the river and its flooded parts. This networks constructed over the network of the river flow will also give rise to the understanding of the cause of the floods and thereby taking proper measures to avoid major losses or minimize losses to an extent

Innovations in Computer Science and Engineering, 2022

In this paper we present zhou's method (DTM) for solving the initial value problems involving... more In this paper we present zhou's method (DTM) for solving the initial value problems involving fifth order ordinary differential equations initial value problems involving fifth order ordinary differential equations we introduce the concept of DTM & applied it to obtain solution of three numerical examples for demonstration. The results are compared with exact solution & DTM method results. There results show that the technique introduced here is accurate & easy to apply. KEYWORDS :-Ordinary differential equitationszhou's Method (DTM), Initial value problem 1.0 Introduction :-The purpose of this paper is to employ the DTM method on examples of ordinary differential equation of fifth order and compared with result obtain by exact solution by using complimentary function & particular integral. In recent years, Bizar J. used for Riccati differential equation(1), Opanuga On numerical solution of systems of ordinary differential equitations by numeriacla analytical method (2), Che...

The data analysis is key parameter in the process optimization. The large data are generated whil... more The data analysis is key parameter in the process optimization. The large data are generated while processes are under consideration. The e-commerce, finance accounting, industrial process planning, industrial production planning, labor planning, inventory planning, etc., are the few names of the sectors and need large data handling for required and/or targeting the final endues and/or services. The different mathematical tools have been used such as AHP, MAHP, WPM, PROMETHEE, VIKOR, Games theory, and curve fitting. However, curve fitting has been used for many industrial applications for the processes planning, inventory planning, labor resources planning, etc. Depending on the data form and ability of researcher, the different curves or lines are used for formulation of the mathematical function. These functions could be straight-line function, second-order polynomial function, third-order polynomial functions, logarithmic, exponential function, etc. This paper discusses the curve...

Over the past many centuries river floods have been a matter of great concern throughout India. I... more Over the past many centuries river floods have been a matter of great concern throughout India. India being a country with varied natural habitats is also fortified with several rivers flowing through almost every state. These rivers mostly have their tributaries playing a major role to reach out the remote places that are difficult to reach by the river itself. However, during the time of monsoon or the rainy season these rivers also act as catastrophe originating instruments and thereby resulting in floods. These floods cause heavy destruction causing financial as well as loss of life at many times. One such incident of the river Yamuna during the time of flood is discussed. This paper involves a mathematical approach in the form of constructing graphical network over the flow patterns of the river and its flooded parts. This networks constructed over the network of the river flow will also give rise to the understanding of the cause of the floods and thereby taking proper measures to avoid major losses or minimize losses to an extent

American Journal of Computational and Applied Mathematics, 2018

In this paper, effective algorithms of finite difference method (FDM) and finite element method (... more In this paper, effective algorithms of finite difference method (FDM) and finite element method (FEM) are designed. The solution of partial differential 2-D Laplace equation in Electrostatics with Dirichlet boundary conditions is evaluated. The electric potential over the complete domain for both methods are calculated. The developed numerical solutions in MATLAB gives results much closer to exact solution when evaluated at different nodes. An error analysis is also presented where the numerical error based on the L2 norm is computed. This error reduces monotonically by reducing the mesh size.

International Journal of Mathematics Trends and Technology

This paper focuses on the use of solving electrostatic one-dimension Poisson differential equatio... more This paper focuses on the use of solving electrostatic one-dimension Poisson differential equation boundary-value problem. Sample problems that introduce the finite element methods are presented here and evaluated with analytical and numerical approaches. These approaches are developed in MATLAB and their solutions are compared and verified. Error analysis is also presented in this paper where the numerical error is compute dusing two different definitions namely the percent error and the error based on the L 2 norm. this numerical error is reduced by increasing in number of elements.

IOP Conference Series: Materials Science and Engineering

International Journal of Mathematics Trends and Technology

International Journal of Mathematics Trends and Technology