Symbolic computation of analytic approximate solutions for nonlinear differential equations with initial conditions

Abstract
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,...

Title of program: NAPA
Catalogue Id: AEJZ_v1_0

Nature of problem
Solve nonlinear differential equations with initial conditions.

Versions of this program held in the CPC repository in Mendeley Data
AEJZ_v1_0; NAPA; 10.1016/j.cpc.2011.08.001

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)

摘要：Adomian 分解法（Adomian decomposition method，简称 ADM）是构建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，结合两步 Adomian 分解法（Two-step Adomian decomposition method，简称 TSADM）与 Pade 技术提出了一种新的算法，旨在构建带有初始条件的非线性微分方程的精确解析近似解。此外，还开发了一个 MAPLE 软件包。

程序名称：NAPA

目录编号：AEJZ_v1_0

问题性质：求解带有初始条件的非线性微分方程。

CPC 数据库中 Mendeley 数据存储的此程序的版本：AEJZ_v1_0；NAPA；10.1016/j.cpc.2011.08.001

此程序已从贝尔法斯特女王大学（1969-2018）的 CPC 程序库中导入。