A Highly Accurate Time–Space Pseudospectral Approximation and Stability Analysis of Two Dimensional Brusselator Model for Chemical Systems

Abstract

In this paper, the authors investigate the numerical solutions of two-dimensional reaction–diffusion equations with Neumann boundary conditions, known as Brusselator model, using Chebyshev pseudospectral method. The proposed methods are established in both time and space to approximate the solutions and prove the stability analysis of the equations. Higher order Chebyshev differential matrix is used in discretizing Brusselator model. The methods convert the Brusselator model into a system ofS algebraic equations, which are solved using Newton–Raphson method and obtained different types of patterns. Error of the proposed method is presented in terms of $$ L_{\infty }$$ and $$ L_{2}$$ error norms. In support of theoretical results, the methods are implemented on two problems and found highly accurate and stable approximations. The detailed comparison of the proposed method with various other methods are also given.