检索结果-南通市图书馆

The Degenerate Form of the adomian polynomials in the Power Series Method for Nonlinear Ordinary Differential Equations

引用

Journal of Mathematics and System Science 2015年第10期5卷 411-428页

作者： Jun-Sheng Duan Randolph Rach School of Sciences Shanghai Institute of Technology Shanghai 201418 P.R. China Emeritus 316 South Maple Street Hartford M14905 7-122 5 U.S.A.

In this paper, we propose a new variation of the adomian polynomials, which we call the degenerate adomian polynomials, for the power series solutions of nonlinear ordinary differential equations with nonseparable nonlinearities. We establish efficient algorithms for the degenerate adomian polynomials. Next we compare the results by the adomian decomposition method using the classic adomian polynomials with the results by the Rach-adomian-Meyers modified decomposition method incorporating the degenerate adomian polynomials, which itself has been shown to be a confluence of the adomian decomposition method and the power series method. Convergence acceleration techniques including the diagonal Pade approximants are considered, and new numeric algorithms for the multistage decomposition are deduced using the degenerate adomian polynomials. Our new technique provides a significant advantage for automated calculations when computing the power series form of the solution for nonlinear ordinary differential equations. Several expository examples are investigated to demonstrate its reliability and efficiency.

关键词： Power series method adomian decomposition method adomian polynomials Modified decomposition method Nonlinear differential equation

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

An Efficient Maple Program for Calculating adomian polynomials

引用

American Journal of Computational Mathematics 2023年第4期13卷 512-523页

作者： Mariam Al-Mazmumy Department of Mathematics and Statistics College of Science University of Jeddah Jeddah Saudi Arabia

The immense quest for proficient numerical schemes for the solution of mathematical models featuring nonlinear differential equations led to the realization of the adomian decomposition method (ADM) in the 80th. Undoubtedly, the solution of nonlinear differential equations using ADM is presided over by the acquisition of adomian polynomials, which are not always easy to find. Thus, the present study proposes easy-to-implement Maple programs for the computation of adomian polynomials. In fact, the proposed algorithms performed remarkably on several test functions, consisting of one- and multi-variable nonlinearities. Moreover, the introduced programs are advantageous in terms of simplicity;coupled with the requirement of less computational time in comparison with what is known in the literature.

关键词： Nonlinear Operators adomian polynomials adomian Decomposition Method Multi-Variable Nonlinearities Maple Package

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Decomposition method for solving parabolic equations in finite domains

引用

Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2005年第10期6卷 1058-1064页

作者： INC Mustafa Department of Mathematics Firat University Elazig 23119Turkey

This paper presents a comparison among adomian decomposition method (ADM), Wavelet-Galerkin method (WGM), the fully explicit (1,7) finite difference technique (FTCS), the fully implicit (7,1) finite difference method (BTCS), (7,7) Crank-Nicholson type finite difference formula (C-N), the fully explicit method (1,13) and 9-point finite difference method, for solving parabolic differential equations with arbitrary boundary conditions and based on weak form functionals in finite domains. The problem is solved rapidly, easily and elegantly by ADM. The numerical results on a 2D transient heat conducting problem and 3D diffusion problem are used to validate the proposed ADM as an effective numerical method for solving finite domain parabolic equations. The numerical results showed that our present method is less time consuming and is easier to use than other methods. In addition, we prove the convergence of this method when it is applied to the nonlinear parabolic equation.

关键词： adomian decomposition method (ADM) adomian polynomials Parabolic differential equations

来源：

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

欢迎您,

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

在线全文

在线全文

在线全文

请选择保存的检索档案：

请选择收藏分类：

通借通还

欢迎您,

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

在线全文

在线全文

在线全文

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：