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A second-order accurate difference scheme for the two-dimensional Burgers' system

✍ Scribed by Pei-Pei Xu; Zhi-Zhong Sun

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
290 KB
Volume
25
Category
Article
ISSN
0749-159X

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✦ Synopsis

Abstract

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. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009

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