Journal of Applied Mathematics and Computation

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Frequency: quarterly ISSN Online: 2576-0653 CODEN: JAMCEZ
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Article http://dx.doi.org/10.26855/jamc.2020.06.003

Direct Approach to Compute a Class of Reaction-Diffusion Equation by a Finite Element Method

Sadia Akter Lima 1, Md. Kamrujjaman 2,3,*, Md. Shafiqul Islam 1

1 Department of Applied Mathematics, University of Dhaka, Dhaka 1000, Bangladesh.

2 Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh.

3 Department of Mathematics and Statistics, University of Calgary, Calgary, AB, Canada.

*Corresponding author: Md. Kamrujjaman, Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh; Department of Mathematics and Statistics, University of Calgary, Calgary, AB, Canada.

Published: May 19,2020

Abstract

In this study, we consider the robust and well known numerical method such as Finite Element Method (FEM) to find the numerical approximation of nonlinear parabolic partial differential equations (PDEs). The key objective of this research paper is to study the numerical solution of the famous FitzHugh-Nagumo equation and Fishers equation with regular and irregular geometrical shapes. The numerical scheme used here is a finite element method (FEM) in a simple and convenient way. We mainly focus to find out the accuracy and acceptance of this method by applying small time step size. To convey the efficiency of this method for solving the nonlinear equation, the results are portrayed both graphically and in tabular form which demonstrate the efficiency of this algorithm. The method can be applied for solving any nonlinear parabolic partial differential equations (PDEs).

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How to cite this paper

Direct Approach to Compute a Class of Reaction-Diffusion Equation by a Finite Element Method

How to cite this paper: Sadia Akter Lima, Md. Kamrujjaman, Md. Shafiqul Islam. (2020) Direct Approach to Compute a Class of Reaction-Diffusion Equation by a Finite Element Method. Journal of Applied Mathematics and Computation, 4(2), 26-33.

DOI: http://dx.doi.org/10.26855/jamc.2020.06.003