A Highly Approximate Pseudo-Spectral Method for the Solution of Convection-Diffusion Equations

Abstract

The main purpose of this paper is to compute a highly accurate numerical solution of two dimensional convection--diffusion equations with variable coefficients by using Legendre pseudo-spectral method based on Legendre-Gauss-Lobatto nodes. The Kronecker product is used here to formulate a linear system of differentiation matrices; this system was reduced to be more accurate with less memory usage. Error analysis with test problems are introduced to show that the suggested scheme of the spectral method has high accuracy.