Jacobi Collocation Technique to Solve Nonlinear Reaction-Diffusion Equation

Abstract

Abstract To analyze the transport phenomena in porous structure, one basically gets nonlinear reaction-diffusion equation. In this article, we have proposed a numerical technique to solve such problems using Legendre collocation technique. In the proposed scheme, Legendre polynomial are used along with operational matrices and spectral collocation method to convert the considered problems in systems of nonlinear algebraic equations that can be solved using Newton-Iteration method. The salient feature of the article is the exhibition of sub-diffusion nature of solution profile for different particular cases in the presence or absence of the source/sink term. The accuracy of the proposed method is exhibited through applying it to two existing problems having exact solutions and compared the results through error analysis which shows the efficiency and high accuracy of the approach.