کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
501789 863647 2012 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Symbolic computation of analytic approximate solutions for nonlinear differential equations with initial conditions
موضوعات مرتبط
مهندسی و علوم پایه شیمی شیمی تئوریک و عملی
پیش نمایش صفحه اول مقاله
Symbolic computation of analytic approximate solutions for nonlinear differential equations with initial conditions
چکیده انگلیسی

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 summaryProgram title: NAPACatalogue identifier: AEJZ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJZ_v1_0.htmlProgram obtainable from: CPC Program Library, Queenʼs University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 4060No. of bytes in distributed program, including test data, etc.: 113 498Distribution format: tar.gzProgramming language: MAPLE R13Computer: PCOperating system: Windows XP/7RAM: 2 GbytesClassification: 4.3Nature 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.


► We present an algorithm to calculate approximations for initial value problems.
► A Maple package NAPA is developed for initial value problems.
► The package NAPA is user-friendly and efficient.
► NAPA has been used to solve initial value problems including the Brusselator Model.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer Physics Communications - Volume 183, Issue 1, January 2012, Pages 106–117
نویسندگان
, , ,