Direct Approach to Compute a Class of Reaction-Diffusion Equation by a Finite Element Method
Sadia Akter Lima, Md. Kamrujjaman, Md. Shafiqul Islam · Journal of Applied Mathematics and Computation · 2020
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 Fisher's 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).