LIE, a PC program for Lie analysis of differential equations
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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是一款独立的个人计算机（PC）程序，用于对单方程或联立方程组形式的常微分方程（ordinary differential equations）与偏微分方程（partial differential equations）开展李群分析（Lie analysis）。该程序基于符号数学语言（symbolic mathematics language）MUMATH编写，可在任意个人计算机上运行。程序包集成了MUMATH的必要组件，为完整且可直接运行的独立程序。此前版本仅支持经典李群分析，用于求解适定微分方程（well-posed differential equations）的点对称性（point symmetries）；本次更新已将功能拓展至接触对称性（contact symmetries）、李-巴克伦对称性（Lie-Bäcklund symmetries，原文后续内容未完整展示）。 程序名称：LIE 4.5版 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（explicit exact solutions）将具有极高的研究价值，而李群分析是目前已知唯一能够系统求解此类精确解的方法。该求解流程已有成熟的理论体系[1-5]，但涉及大量符号运算（symbolic calculation），更适合通过计算机完成。 存放在Mendeley数据库（Mendeley Data）的CPC程序库中的该程序版本： ACPB_v1_0；LIE 4.1版；DOI:10.1016/0010-4655(93)90007-Y ACPB_v2_0；LIE 4.5版；DOI:10.1016/0010-4655(96)00069-0 本程序源自贝尔法斯特女王大学（Queen's University Belfast）托管的CPC程序库（1969-2019）
