New Parallel Algorithm for Convection-Dominated Diffusion Equation

Abstract

A new parallel algorithm for convection-dominated diffusion equation is proposed. To derive an approximate solution of the problem at the same time level, we use two domain decomposition methods. The average of the solutions obtained is set to be new numerical solution. The algorithm demonstrates a high accuracy and is suitable for parallel computing. Approximate solution of two-dimensional convection-dominated diffusion equations is also considered. Numerical examples show the efficiency and reliability of the algorithm.