A Second-Order Accurate Difference Scheme for the Two-Dimensional Burgers' System

作者：Xu Pei Pei; Sun Zhi Zhong^*

来源：Numerical Methods for Partial Differential Equations, 2009, 25(1): 172-194.

DOI：10.1002/num.20335

• Burgers' system
• finite difference scheme
• convergence
• solvability
• stability

In this article, a Crank-Nicolson-type finite difference scheme for the two-dimensional Burgers' system is presented. The existence of the difference solution is shown by Brouwer fixed-point theorem. The uniqueness of the difference solution and the stability and L(2) convergence of the difference scheme are proved by energy method. An iterative algorithm for the difference scheme is given in detail. Furthermore, a linear predictor-corrector method is presented. The numerical results show that the predictor-corrector method is also convergent with the convergence order of two in both time and space. At last. some comments are provided for the backward Euler scheme.

• 出版日期2009-1
• 单位东南大学