Analytic Travelling Wave Solutions and Numerical Analysis of Fisher’s Equation via Explicit-Implicit FDM
Asif Ahmed
Department of Mathematics, University of Dhaka, Dhaka-1000, Bangladesh.
Md. Kamrujjaman *
Department of Mathematics, University of Dhaka, Dhaka-1000, Bangladesh.
*Author to whom correspondence should be addressed.
Abstract
We study the nonlinear parabolic Fisher’s equations for travelling wave solutions. The analyses focus on to describe the analytic solution in the spatial pattern of travelling wave solutions; especially the solutions are characterized in invariant with respect to translation in space. There are two phases in the work: in the first stage, we analyze dimensional reaction-diffusion equation with logistic type growth while in the second phase the non-dimensional equation known as Fishers’ equation is studied numerically. To investigate the results numerically, we select the explicit-implicit finite difference method (FDM) and the approximate solutions are compared with the exact solution in different time steps.
Keywords: Travelling waves, analytic solution, Explicit-Implicit FDM, Fisher’s equation, numerical analysis