Numerical solution of two dimensional reaction-diffusion equation using operational matrix method based on genocchi polynomial – Part II: Error bound and stability analysis

Abstract

In this article, an operational matrix method with Genocchi polynomials is applied to solve a two dimensional space-time fractional order nonlinear reaction-diffusion equation. Applying collocation method and using the said matrix, fractional order non-linear partial differential equation is reduced to a system of algebraic equations, which have been solved using Newton iteration method. The salient features of the article are finding the stability analysis and error bound of the proposed scheme and pictorial presentations of the numerical solution of the concerned equation for different particular cases to show the effect of reaction term on the solution profile and also the change of its behaviour when the system approaches from standard order to fractional order. The accuracy of our proposed method is validated through the error analysis of the obtained numerical results with the existing analytical results for two particular cases of the concerned fractional order nonlinear model. © 2020 Editura Academiei Romane. All rights reserved.