LIE, a PC program for Lie analysis of differential equations

Abstract
LIE is a self-contained PC program for the Lie analysis of ordinary or partial differential equations, either a single equation or a simultaneous set. It is written in the symbolic mathematics language MUMATH and will run on any PC. It comes as a complete program that incorporates the necessary parts of MUMATH and is ready to run. The previous version was for classical Lie analysis, finding the point symmetries of well-posed differential equations. This is now extended to contact, Lie-Backlun...

Title of program: LIE version 4.5
Catalogue Id: ACPB_v2_0 [ADDT]

Nature of problem
Differential equations are omnipresent in most departments of science. Explicit exact solutions are of great value when they exist and Lie analysis is the only systematic method of finding them. The procedure is well-known [1-5] but involves a large amount of symbolic calculation that is better done by computer.

Versions of this program held in the CPC repository in Mendeley Data
ACPB_v1_0; LIE version 4.1; 10.1016/0010-4655(93)90007-Y
ACPB_v2_0; LIE version 4.5; 10.1016/0010-4655(96)00069-0

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

摘要
LIE是一款可独立运行的个人计算机（PC）程序，用于开展常微分方程或偏微分方程（单方程或联立方程组）的李（Lie）分析。该程序采用符号数学语言MUMATH编写，可在任意个人计算机上运行。其作为完整程序包发布，内置所需的MUMATH组件，可直接启动运行。此前版本仅支持经典李分析，用于求解适定微分方程的点对称性；本次更新已将功能拓展至接触对称性与李-巴克伦（Lie-Bäcklund）分析……（原文未收尾）

程序名称：LIE 版本4.5
目录编号：ACPB_v2_0 [ADDT]

问题属性
微分方程广泛存在于绝大多数科学研究领域中。若能获取其显式精确解，将具备极高的研究与应用价值，而李分析是目前唯一可系统求解此类解的方法。该求解流程已有成熟文献支撑[1-5]，但需完成大量符号计算工作，更适合由计算机自动执行。

孟德尔莱（Mendeley）数据平台的CPC程序库中收录的该程序版本：
ACPB_v1_0；LIE 4.1版本；DOI:10.1016/0010-4655(93)90007-Y
ACPB_v2_0；LIE 4.5版本；DOI:10.1016/0010-4655(96)00069-0

本程序源自贝尔法斯特女王大学托管的CPC程序库（1969-2019）