华东师范大学学报(自然科学版) ›› 2011, Vol. 2011 ›› Issue (3): 100-110.

• 计算机科学与技术 • 上一篇    下一篇

同伦分析方法的推广及其实现

朱 伟; 柳银萍   

  1. 华东师范大学 计算机科学与技术系, 上海 200241
  • 收稿日期:2010-07-01 修回日期:2010-10-01 出版日期:2011-05-25 发布日期:2011-05-25
  • 通讯作者: 柳银萍

Extension and implementation of the homotopy analysis method

ZHU Wei; LIU Yin-ping   

  1. Department of Computer Science and Technology, East China Normal University, Shanghai 200241, China
  • Received:2010-07-01 Revised:2010-10-01 Online:2011-05-25 Published:2011-05-25
  • Contact: LIU Yin-ping

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摘要： 基于Rach对Adomian多项式的新定义, 推广了同伦分析方法. 给出了三种Rm的新定义, 通过分析可知它们的展开速度优于传统同伦分析方法. 这些方法的引入为求解非线性微分方程提供了新的思路, 特别是当传统同伦分析法收敛较慢时, 可以尝试使用. 在此基础上, 基于Maple 10平台对常微分方程实现了传统同伦分析方法和推广方法的通用计算程序, 使用户可以更方便地使用.

关键词: 同伦分析法, Adomian分解法, Adomian多项式, Taylor展开序列, 非线性微分方程, 同伦分析法, Adomian分解法, Adomian多项式, Taylor展开序列, 非线性微分方程

Abstract: The homotopy analysis method (HAM) was extended based on the new definition of the Adomian Polynomials proposed by Rach in 2008. Three new kinds of Rm in HAM were defined. By analyzing we know that their expanding speeds are higher than that of the original HAM. These methods provide us more choices to deal with differential equations, especially when the original HAM does not work well. A Maple package was developed to automatically solve ordinary differential system with all of these methods conveniently.

Key words: Adomian decomposition method, Adomian polynomials, Taylor expansion series, nonlinear differential equations, homotopy analysis method, Adomian decomposition method, Adomian polynomials, Taylor expansion series, nonlinear differential equations

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