Symbolic computation of analytic approximate solutions for nonlinear differential equations with initial conditions
Symbolic computation of analytic approximate solutions for nonlinear differential equations with initial conditions
复制标题
具有初始条件的非线性微分方程解析近似解的符号计算
DOI：
10.1016/j.cpc.2011.08.001
复制
发表时间：
2012
影响因子：
6.3
通讯作者：
Zhibin Li
中科院分区：
文献类型：
--
作者：
Yezhi Lin;Yinping Liu;Zhibin Li
Adomian分解法是构造非线性微分方程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，将两步Adomian分解法（TSADM）与pad<s:1>技术相结合，提出了一种构造具有初始条件的非线性微分方程精确解析逼近的新算法。在此基础上，开发了一个方便、高效的MAPLE软件包。只需要输入系统、初始条件和几个必要的参数，我们的包就会在几秒钟内自动给出解析近似解。给出了几种不同类型的例子来说明该包的有效性。我们的程序为科学和工程中处理初值问题提供了一个有用且易于使用的工具。项目摘要：项目名称：NAPA目录标识符：AEJZ_v1_0项目摘要URL:http://cpc.cs.qub.ac.uk/summaries/AEJZ_v1_0.html项目可从：北爱尔兰贝尔法斯特女王大学CPC项目图书馆获得许可条款：标准CPC许可，http://cpc.cs.qub.ac.uk/licence/licence.html号。分布式程序的行数，包括测试数据等；分布程序的字节数，包括测试数据等：113 498分布格式：tar.gz编程语言：MAPLE R13计算机：PC操作系统：Windows XP/7内存：2gb分类：4.3问题性质：求解具有初始条件的非线性微分方程。解决方法：Adomian分解法和pad<s:1>法。运行时间：在程序的日常使用中最多几秒钟。特殊任务可能需要几分钟。
The Adomian decomposition method (ADM) is one of the most effective methods for constructing analytic approximate solutions of nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials, and the two-step Adomian decomposition method (TSADM) combined with the Padé technique, a new algorithm is proposed to construct accurate analytic approximations of nonlinear differential equations with initial conditions. Furthermore, a MAPLE package is developed, which is user-friendly and efficient. One only needs to input a system, initial conditions and several necessary parameters, then our package will automatically deliver analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the validity of the package. Our program provides a helpful and easy-to-use tool in science and engineering to deal with initial value problems. PROGRAM SUMMARY: Program title: NAPA Catalogue identifier: AEJZ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJZ_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 4060 No. of bytes in distributed program, including test data, etc.: 113 498 Distribution format: tar.gz Programming language: MAPLE R13 Computer: PC Operating system: Windows XP/7 RAM: 2 Gbytes Classification: 4.3 Nature of problem: Solve nonlinear differential equations with initial conditions. Solution method: Adomian decomposition method and Padé technique. Running time: Seconds at most in routine uses of the program. Special tasks may take up to some minutes.
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DOI：
10.1016/j.sbspro.2010.12.090
发表时间：
2010
期刊：
Procedia - Social and Behavioral Sciences
影响因子：
--
作者：
Md. Sazzad Hossien Chowdhury;T. Hassan;S. Mawa
通讯作者：
Md. Sazzad Hossien Chowdhury;T. Hassan;S. Mawa
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：
Wazwaz, AM
通讯作者：
Wazwaz, AM
DOI：
10.1016/s0096-3003(03)00629-5
发表时间：
2004-05
期刊：
Appl. Math. Comput.
影响因子：
--
作者：
E. Babolian;S. Javadi
通讯作者：
E. Babolian;S. Javadi