Numerical Solution of Reaction–Diffusion Equations with Convergence Analysis

Abstract

In this manuscript, we implement a spectral collocation method to find the solution of the reaction–diffusion equation with some initial and boundary conditions. We approximate the solution of equation by using a two-dimensional interpolating polynomial dependent to the Legendre–Gauss–Lobatto collocation points. We fully show that the achieved approximate solutions are convergent to the exact solution when the number of collocation points increases. We demonstrate the capability and efficiency of the method by providing four numerical examples and comparing them with other available methods.