| 非线性微分方程解析近似解的自动推导 |
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| 引用本文： | 褚红梅,刘颖,柳银萍.非线性微分方程解析近似解的自动推导[J].华东师范大学学报(自然科学版),2010,2010(6):125-136. |
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| 作者姓名： | 褚红梅 刘颖 柳银萍 |
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| 作者单位： | 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 |
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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.
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| 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 |
| 收稿时间： | 2010-1-1 |
| 修稿时间： | 2010-4-1 |
Automated derivation for analytical approximate solutions to nonlinear differential equations |
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| CHU Hong-mei,LIU Ying,LIU Yin-ping.Automated derivation for analytical approximate solutions to nonlinear differential equations[J].Journal of East China Normal University(Natural Science),2010,2010(6):125-136. |
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| Authors: | CHU Hong-mei LIU Ying LIU Yin-ping |
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| Institution: | 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 |
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| 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. |
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| Keywords: | symbolic computation Adomian decomposition method(ADM) Adomian polynomials Adomian-Pade approximants |
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