Symbolic computation of analytic approximate solutions for nonlinear differential equations with boundary conditions
Symbolic computation of analytic approximate solutions for nonlinear differential equations with boundary conditions
复制标题
具有边界条件的非线性微分方程解析近似解的符号计算
DOI：
10.1016/j.amc.2013.06.076
复制
发表时间：
2013-10
影响因子：
4
通讯作者：
Zhibin Li
中科院分区：
文献类型：
--
作者：
Yezhi Lin;Yinping Liu;Zhibin Li
Adomian 分解方法 (ADM) 是构造解析近似解的最有效方法之一。本文基于Adomian多项式的新定义和二重分解方法，提出了一种新的算法来构造具有（耦合）边界条件的非线性微分方程的解析近似。此外，还开发了 MAPLE 软件包来实现我们的新算法，该算法用户友好且高效。只需输入系统、边界条件和几个必要的参数，我们的软件包就会在几秒钟内提供解析近似解。给出了几种不同类型的非线性示例来说明我们的软件包的范围并证明其有效性，特别是对于非线性多阶和多点边值问题。我们的软件包提供了一个有用且易于使用的科学和工程工具来处理最常遇到的边值问题。这个MAPLE包可以在网站上免费下载：http://www.cs.ecnu.edu.cn/∼lizb/index.htm。
The Adomian decomposition method (ADM) is one of the most effective methods for constructing analytic approximate solutions. In this paper, based on the new definitions of the Adomian polynomials, and the double decomposition method, a new algorithm is proposed to construct analytic approximations for nonlinear differential equations with (coupled) boundary conditions. Furthermore, a MAPLE software package is developed to implement our new algorithm, which is user-friendly and efficient. One only needs to input the system, boundary conditions and several necessary parameters, then our package will deliver the analytic approximate solution within a few seconds. Several different types of nonlinear examples are given to illustrate the scope and demonstrate the validity of our software package, especially for nonlinear multi-order and multi-point boundary value problems. Our package provides a helpful and easy-to-use tool in science and engineering to deal with the most frequently encountered boundary value problems. This MAPLE package is free to download on the website: http://www.cs.ecnu.edu.cn/∼lizb/index.htm.
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DOI：
10.1016/j.camwa.2009.12.002
发表时间：
2010-03
期刊：
Comput. Math. Appl.
影响因子：
--
作者：
Javed Ali;Saeed Islam;Sirajul Islam;G. Zaman
通讯作者：
Javed Ali;Saeed Islam;Sirajul Islam;G. Zaman
DOI：
10.1016/s0045-7825(99)00018-3
发表时间：
1999-08-03
影响因子：
7.2
作者：
He, JH
通讯作者：
He, JH
影响因子：
4
作者：
Geng, Fazhan;Cui, Minggen
通讯作者：
Cui, Minggen
影响因子：
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作者：
K. Abbaoui;Y. Cherruault;V. Seng
通讯作者：
K. Abbaoui;Y. Cherruault;V. Seng
影响因子：
2.3
作者：
Yue-Tzu Yang;C. Chang;Cha’o-Kuang Chen
通讯作者：
Yue-Tzu Yang;C. Chang;Cha’o-Kuang Chen