Bimal Datta - Academia.edu (original) (raw)

Papers by Bimal Datta

American Journal of Mathematics and Statistics, 2015

Mathematical model is a very useful tool to understand and analyse the dynamics of diseases. Here... more Mathematical model is a very useful tool to understand and analyse the dynamics of diseases. Here we present a non-linear mathematical model which investigates the spread and control of HIV in different populations. Present study fitted the model, which exhibits two equilibrium points namely, the disease free equilibrium and the endemic equilibrium point. The global stability of these equilibrium points is also investigated. The model is analysed by using the basic reproduction number ���� 0.

Numerical differential equations studies the methods for finding numerical approximations to the ... more Numerical differential equations studies the methods for finding numerical approximations to the solutions of differential equations, occur in many scientific disciplines, for instance in physics, chemistry, biology, and economics. Because of its various applications, this is often viewed as a discipline in and of itself. In this paper we develop a numerical simulator for solving ordinary differential equations (ODEs). This simulator is incorporated with a combination of Euler, modified Euler and Runge-Kutta second and fourth order methods.

The work being presented in this thesis is devoted to investigate the different techniques for so... more The work being presented in this thesis is devoted to investigate the different techniques for solving Quadratic Programming Problems (QPP) and Non-Linear Programming Problems (NLPP). We first develop a technique to generalize the traditional simplex method for solving a special type (Quasi-concave) QPP in which the objective function can be factorized. We then investigate three well known methods in Operation Research known as Lagrange's method, Karush-Kuhn-Tucker (KKT) method and Wolf's method for solving QP and NLP problems. Graphical representation of the above three methods are also demonstrated along with their merits and demerits. We implement Lagrange's method for solving any type of NLPP. For this, we develop a computer technique along with algorithm. We then develop another computer technique for the implementation of KKT method for solving any NLPP. We also modify Wolf's method to solve any type of QP problems. For this, we develop a computer technique. Al...

HIV/AIDS and Malaria are the two great threats for human being. These are causing a lot of death ... more HIV/AIDS and Malaria are the two great threats for human being. These are causing a lot of death every year. Here comprehensive mathematical techniques have been used to analyze the co-infection of HIV-Malaria. A mathematical model of co-infection has been formulated. It is found that, using the next generation matrices, the disease free equilibrium point is locally asymptotically stable when the reproduction number is less than unity and unstable when reproduction number is greater than unity. Centre manifold theory is used to show that the HIV/AIDS-malaria co-infection model`s endemic equilibrium point is locally asymptotically stable when the associated reproduction numbers are less than unity. It has shown that, reduction of sexual activities among the HIV infected population will reduces the HIV/AIDS in the society. As well as it will also reduce the mortality rate of HIV- malaria co-infection.

Global Journal of Researches in Engineering, Dec 31, 2015

Journal of Scientific Research and Reports

In this letter, we seek new traveling wave solutions to Burgers equation via a new approach of im... more In this letter, we seek new traveling wave solutions to Burgers equation via a new approach of improved) / (G G -expansion method. We handle the calculations with the aid of computer software Maple-13. As a result, many periodic and soliton like solutions have been achieved in terms of the hyperbolic functions, trigonometric functions, exp-functions and rational function solutions. The method is very simple for solving nonlinear evolution equations (NLEEs). Further, both two and three-dimensional plots of the obtained wave solutions are also given to imagine the dynamics of the equation.

SpringerPlus, 2014

In this paper, we have described two dreadfully important methods to solve nonlinear partial diff... more In this paper, we have described two dreadfully important methods to solve nonlinear partial differential equations which are known as exp-function and the exp(−ϕ(ξ))-expansion method. Recently, there are several methods to use for finding analytical solutions of the nonlinear partial differential equations. The methods are diverse and useful for solving the nonlinear evolution equations. With the help of these methods, we are investigated the exact travelling wave solutions of the Vakhnenko-Parkes equation. The obtaining soliton solutions of this equation are described many physical phenomena for weakly nonlinear surface and internal waves in a rotating ocean. Further, three-dimensional plots of the solutions such as solitons, singular solitons, bell type solitary wave i.e. non-topological solitons solutions and periodic solutions are also given to visualize the dynamics of the equation.

International Journal of Research in Engineering and Technology, 2013

This work proposes the coefficients for Angstrom-Prescott type of model for the estimation of glo... more This work proposes the coefficients for Angstrom-Prescott type of model for the estimation of global solar radiation in Dhaka, Bangladesh using the relative sunshine duration alongside the measured global solar radiation data (1983-2010). The model constants a and b obtained in this investigation for Dhaka are 0.23 and 0.57 respectively. The correlation coefficient of 87% between the clear sky index and relative sunshine duration, as well as the coefficient of determination of 75.7 obtained shows that this model fits the data very well. Consequently, the developed model in this work can be used with confidence for Dhaka and other locations with similar climate conditions.

Abstract: Numerical analysis concerns the development of algorithms for solving various types o... more Abstract:
Numerical analysis concerns the development of algorithms for solving various types of problems of mathematics; it is a vast-ranging field having deep interaction with computer science, mathematics, engineering, and the sciences. Numerical analysis mainly consists of Numerical Integration, Numerical Differentiation and finding Roots numerically.

American Journal of Mathematics and Statistics, 2015

Mathematical model is a very useful tool to understand and analyse the dynamics of diseases. Here... more Mathematical model is a very useful tool to understand and analyse the dynamics of diseases. Here we present a non-linear mathematical model which investigates the spread and control of HIV in different populations. Present study fitted the model, which exhibits two equilibrium points namely, the disease free equilibrium and the endemic equilibrium point. The global stability of these equilibrium points is also investigated. The model is analysed by using the basic reproduction number ���� 0.

Numerical differential equations studies the methods for finding numerical approximations to the ... more Numerical differential equations studies the methods for finding numerical approximations to the solutions of differential equations, occur in many scientific disciplines, for instance in physics, chemistry, biology, and economics. Because of its various applications, this is often viewed as a discipline in and of itself. In this paper we develop a numerical simulator for solving ordinary differential equations (ODEs). This simulator is incorporated with a combination of Euler, modified Euler and Runge-Kutta second and fourth order methods.

The work being presented in this thesis is devoted to investigate the different techniques for so... more The work being presented in this thesis is devoted to investigate the different techniques for solving Quadratic Programming Problems (QPP) and Non-Linear Programming Problems (NLPP). We first develop a technique to generalize the traditional simplex method for solving a special type (Quasi-concave) QPP in which the objective function can be factorized. We then investigate three well known methods in Operation Research known as Lagrange's method, Karush-Kuhn-Tucker (KKT) method and Wolf's method for solving QP and NLP problems. Graphical representation of the above three methods are also demonstrated along with their merits and demerits. We implement Lagrange's method for solving any type of NLPP. For this, we develop a computer technique along with algorithm. We then develop another computer technique for the implementation of KKT method for solving any NLPP. We also modify Wolf's method to solve any type of QP problems. For this, we develop a computer technique. Al...

HIV/AIDS and Malaria are the two great threats for human being. These are causing a lot of death ... more HIV/AIDS and Malaria are the two great threats for human being. These are causing a lot of death every year. Here comprehensive mathematical techniques have been used to analyze the co-infection of HIV-Malaria. A mathematical model of co-infection has been formulated. It is found that, using the next generation matrices, the disease free equilibrium point is locally asymptotically stable when the reproduction number is less than unity and unstable when reproduction number is greater than unity. Centre manifold theory is used to show that the HIV/AIDS-malaria co-infection model`s endemic equilibrium point is locally asymptotically stable when the associated reproduction numbers are less than unity. It has shown that, reduction of sexual activities among the HIV infected population will reduces the HIV/AIDS in the society. As well as it will also reduce the mortality rate of HIV- malaria co-infection.

Global Journal of Researches in Engineering, Dec 31, 2015

Journal of Scientific Research and Reports

In this letter, we seek new traveling wave solutions to Burgers equation via a new approach of im... more In this letter, we seek new traveling wave solutions to Burgers equation via a new approach of improved) / (G G -expansion method. We handle the calculations with the aid of computer software Maple-13. As a result, many periodic and soliton like solutions have been achieved in terms of the hyperbolic functions, trigonometric functions, exp-functions and rational function solutions. The method is very simple for solving nonlinear evolution equations (NLEEs). Further, both two and three-dimensional plots of the obtained wave solutions are also given to imagine the dynamics of the equation.

SpringerPlus, 2014

In this paper, we have described two dreadfully important methods to solve nonlinear partial diff... more In this paper, we have described two dreadfully important methods to solve nonlinear partial differential equations which are known as exp-function and the exp(−ϕ(ξ))-expansion method. Recently, there are several methods to use for finding analytical solutions of the nonlinear partial differential equations. The methods are diverse and useful for solving the nonlinear evolution equations. With the help of these methods, we are investigated the exact travelling wave solutions of the Vakhnenko-Parkes equation. The obtaining soliton solutions of this equation are described many physical phenomena for weakly nonlinear surface and internal waves in a rotating ocean. Further, three-dimensional plots of the solutions such as solitons, singular solitons, bell type solitary wave i.e. non-topological solitons solutions and periodic solutions are also given to visualize the dynamics of the equation.

International Journal of Research in Engineering and Technology, 2013

This work proposes the coefficients for Angstrom-Prescott type of model for the estimation of glo... more This work proposes the coefficients for Angstrom-Prescott type of model for the estimation of global solar radiation in Dhaka, Bangladesh using the relative sunshine duration alongside the measured global solar radiation data (1983-2010). The model constants a and b obtained in this investigation for Dhaka are 0.23 and 0.57 respectively. The correlation coefficient of 87% between the clear sky index and relative sunshine duration, as well as the coefficient of determination of 75.7 obtained shows that this model fits the data very well. Consequently, the developed model in this work can be used with confidence for Dhaka and other locations with similar climate conditions.

Abstract: Numerical analysis concerns the development of algorithms for solving various types o... more Abstract:
Numerical analysis concerns the development of algorithms for solving various types of problems of mathematics; it is a vast-ranging field having deep interaction with computer science, mathematics, engineering, and the sciences. Numerical analysis mainly consists of Numerical Integration, Numerical Differentiation and finding Roots numerically.