On the numerical solution of Fisher's equation by an efficient algorithm based on multiwavelets

Abstract

<abstract> <p>In this work, we design, analyze, and test an efficient algorithm based on the finite difference method and wavelet Galerkin method to solve the well known Fisher's equation. We employed the Crank-Nicolson scheme to discretize the time interval into a finite number of time steps, and this gives rise to an ordinary differential equation at each time step. To solve this ODE, we utilize the multiwavelets Galerkin method. The $ L^2 $ stability and convergence of the scheme have been investigated by the energy method. Illustrative examples are provided to verify the efficiency and applicability of the method.</p> </abstract>