A class of high-order compact difference schemes for solving the Burgers’ equations

摘要

In this paper, a class of high-order compact difference method is introduced for solving the Burgers’ equations. Firstly, a linear high-order compact difference scheme is proposed to solve the one-dimensional Burgers’ equation. The scheme is fourth-order accurate in space and second-order accurate in time. Linear stability analysis is conducted to show the scheme is conditionally stable. Because only three grid points are involved in each time level, Thomas algorithm can be directly used to solve the tridiagonal linear system. Then, this method is extended to solve the two-dimensional and three-dimensional coupled Burgers’ equations. Numerical experiments are carried out to demonstrate the accuracy and dependability of the present method.