文献类型：期刊文献

英文题名：Numerical solutions of partial differential equations by discrete homotopy analysis method

作者：Zhu, Hongqing[1];Shu, Huazhong[2];Ding, Meiyu[1]

机构：[1]E China Univ Sci & Technol, Dept Elect & Commun Engn, Shanghai 200237, Peoples R China;[2]Southeast Univ, Sch Comp Sci & Engn, Nanjing 210096, Peoples R China

年份：2010

卷号：216

期号：12

起止页码：3592

外文期刊名：APPLIED MATHEMATICS AND COMPUTATION

收录：;EI(收录号：20102513018613);WOS:【SCI-EXPANDED(收录号:WOS:000278919800019)】；

基金：This work has been supported by National Natural Science Foundation of China under Grant No. 60975004. The authors thank the anonymous referees for their helpful comments and suggestions.

语种：英文

外文关键词：Discrete homotopy analysis method; Crank-Nicolson; Burgers' equations; Finite difference scheme; Diffusion equation; Convergence region

摘要：This paper introduces a discrete homotopy analysis method (DHAM) to obtain approximate solutions of linear or nonlinear partial differential equations (PDEs). The DHAM can take the many advantages of the continuous homotopy analysis method. The proposed DHAM also contains the auxiliary parameter (h) over bar, which provides a simple way to adjust and control the convergence region of solution series. The convergence of the DHAM is proved under some reasonable hypotheses, which provide the theoretical basis of the DHAM for solving nonlinear problems. Several examples, including a simple diffusion equation and two-dimensional Burgers' equations, are given to investigate the features of the DHAM. The numerical results obtained by this method have been compared with the exact solutions. It is shown that they are in good agreement with each other. (C) 2010 Elsevier Inc. All rights reserved.