A Class of High-precision Finite Difference Parallel Algorithms for Convection Equations

Abstract

Convection equation is an important type of mathematical model to describe a variety of physical phenomena. The research on its numerical analysis methods has been the focus of many researchers. Evans [1] firstly proposed the group explicit method for solving the convection equation. Other researchers, including Jingliang Chen [2], Jinfu Lu [3], and Chengri Jin [4] etc., then further improved Evans’s work. Most existing group explicit methods cannot achieve the high accuracy and are limited to second order accuracy. Based on alternating group explicit method’s idea, Evans [5] proposed an alternating group explicit iteration method for solving the parabolic equation. This method not only has good absolute stability and accuracy, it is also suitable for parallel computing. Based on this method, Bolin Zhang [6], Rohallah Tavakoli [7] has proposed several algorithms which could achieve absolute stability and high accuracy. This works integrates the grouping explicit method with numerical boundary conditions and proposes an alternating group explicit iteration method with high accuracy for solving the initial-boundary value problem of convection equations. Our method’s accuracy reaches to four order. Experimental results show the promising performance of our method compared to other existing methods.