Computer algebra application for determining Lie and Lie-Bäcklund symmetries of differential equations
نویسندگان
چکیده
منابع مشابه
Computer Algebra Application for Determining Lie and Lie-Bäcklund Symmetries of Differential Equations
The application of computer algebra for determining Lie and Lie–Bäcklund (LB) symmetries of differential equations is considered. Algorithms for calculating the symmetries are developed and implemented on the basis of computer algebra systems REDUCE, AMP and FORMAC. The most effective and advanced program is written in FORMAC. It finds LB symmetries completely automatically. In many cases the p...
متن کاملReduction of Differential Equations by Lie Algebra of Symmetries
The paper is devoted to an application of Lie group theory to differential equations. The basic infinitesimal method for calculating symmetry group is presented, and used to determine general symmetry group of some differential equations. We include a number of important applications including integration of ordinary differential equations and finding some solutions of partial differential equa...
متن کاملLie Symmetries of Differential Equations by Computer Algebra
Secondly combining group theory and singularity analysis we obtained some information about the similarity solutions of the fourth order generalized Boussinesq equation GBE4. It has been shown that this equation possess a three dimensional Lie algebra of the point symmetries and the similarity reductions due to these symmetries have been obtained.
متن کاملLie Symmetries of Differential Equations Byco~uteralgebra
In this paper we restrict ourselves to Lie point symmetries an applications to the fourth order generalized Burgers equation GBE4. Using computer programs under the computer algebra package MATHEMATIC A we find a three dimensional solvable Lie algebra of point symmetries of the GBE4 equation. The similarity reductions due to these symmetries have also been obtained. The idea of applying Lie gro...
متن کاملApplication of the Lie Symmetry Analysis for second-order fractional differential equations
Obtaining analytical or numerical solution of fractional differential equations is one of the troublesome and challenging issue among mathematicians and engineers, specifically in recent years. The purpose of this paper Lie Symmetry method is developed to solve second-order fractional differential equations, based on conformable fractional derivative. Some numerical examples are presented to il...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 1989
ISSN: 0747-7171
DOI: 10.1016/s0747-7171(89)80043-4