Poisson, Helmholtz and Convection 2D Unsteady Equations by Finite Difference Method of O(Δx⁶)

Abstract

This paper presents the numerical solution of transient two-dimensional convection-diffusion-reactions using the Sixth-Order Finite Difference Method. Considering the extension of the Taylor series, the first and second order derivatives from this physical problem are discretized with O(Δx6) accuracy. Using the L and L2 norm, the numerical solution is compared with some examples that have an analytical solution.