华东师范大学学报(自然科学版) ›› 2010, Vol. 2010 ›› Issue (6): 125-136.

• 应用数学与基础数学 • 上一篇    下一篇

非线性微分方程解析近似解的自动推导

褚红梅1, 刘 颖2, 柳银萍1   

  1. 1. 华东师范大学计算机科学技术系, 上海 200241 2. 上海音乐学院附属中等专科音乐学校文化科, 上海 200031
  • 收稿日期:2010-01-01 修回日期:2010-04-01 出版日期:2010-11-25 发布日期:2010-11-25
  • 通讯作者: 柳银萍

Automated derivation for analytical approximate solutions to nonlinear differential equations

CHU Hong-mei 1, LIU Ying 2, LIU Yin-ping 1

  

  1. 1. Department of Computer Science and Technology, East China Normal University, Shanghai 200241, China; 2. Department of Culture, Secondary Specialized Music School Affiliated Shanghai Music Institute, Shanghai 200031, China
  • Received:2010-01-01 Revised:2010-04-01 Online:2010-11-25 Published:2010-11-25
  • Contact: LIU Yin-ping

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摘要： 基于R. C. Rach归纳提出的关于Adomian多项式的四种新算法, 在计算机代数系统 Maple
平台上开发了非线性定解系统解析近似解的自动推导软件包 NAPA, 该软件包在完全实现 Adomian 分解法的基础上, 也嵌入了Pade 有理逼近技术. 因此, NAPA 可自动推导出非线性边值问题更准确的解析近似解. 同时, 该软件包也可直观地比较这四种算法各自的优缺点. 另外, NAPA 软件包的用户界面很友好, 有些结果可以图示的方式直观给出. 最后通过几个实例来说明 NAPA 的有效性和灵活性.

关键词: 符号计算, Adomian分解方法, Adomian多项式, Adomian-Pade近似, 符号计算, Adomian分解方法, Adomian多项式, Adomian-Pade近似

Abstract: Based on four kinds of Adomian polynomials algorithms proposed by R. C. Rach, a package NAPA was developed on Maple 12. The interface of NAPA is user-friendly. As long as one input a differential system with boundary or initial conditions, NAPA can entirely automatically output more accurate approximating solutions. Finally, two different type of examples were given to demonstrate the effectiveness of the package.

Key words: Adomian decomposition method(ADM), Adomian polynomials, Adomian-Pade approximants, symbolic computation, Adomian decomposition method(ADM), Adomian polynomials, Adomian-Pade approximants

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