A MAPLE program for the generation of the Lie-series solution of systems of non-linear ordinary differential equations

Abstract The Lie series is a power series in which the initial conditions are part of the constant coefficients of the series. This property makes the Lie series appropriate for the study of systems of differential equations that exhibit chaotic behavior and, therefore, are sensitive to initial conditions. We present the theory behind the Lie series, a MAPLE program capable of handling single as well as systems of ODE's, several examples of the application of the program to linear and non-linear probl... Title of program: LIESER Catalogue Id: ACBT_v1_0 Nature of problem The Lie-series solution of systems of differential equations that represent physical phenomena can lead to better understanding of the phenomena. It is of special importance for chaotic systems because it contains the initial conditions as part of the coefficients in the series. Versions of this program held in the CPC repository in Mendeley Data ACBT_v1_0; LIESER; 10.1016/0010-4655(92)90058-7 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

摘要 李级数（Lie series）是一类幂级数，其初始条件作为该级数常系数的一部分。这一特性使得李级数适用于研究表现出混沌行为、因此对初始条件敏感的微分方程组。本文阐述了李级数的相关理论，提供了一款可处理单个常微分方程（Ordinary Differential Equation，简称ODE）及常微分方程组的MAPLE程序，并展示了该程序在线性与非线性问题中的若干应用示例……
程序名称：LIESER
目录编号：ACBT_v1_0
问题特性 针对表征物理现象的微分方程组，采用李级数求解可增进对该类现象的理解，这对于混沌系统尤为关键，因其将初始条件作为级数系数的一部分纳入其中。
Mendeley数据中的CPC程序库存档版本：ACBT_v1_0; LIESER; 10.1016/0010-4655(92)90058-7
本程序源自贝尔法斯特女王大学馆藏的CPC程序库（1969-2019年）