Programs in Physics & Physical Chemistry
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Programs in Physics & Physical Chemistry |
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| Manuscript Title: GeM software package for computation of symmetries and conservation laws of differential equations | ||
| Authors: Alexei F. Cheviakov | ||
| Program title: GeM [1] | ||
| Catalogue identifier: ADYK_v1_0 Distribution format: tar.gz | ||
| Journal reference: Comput. Phys. Commun. 176(2007)48 | ||
| Programming language: Maple 9.5. | ||
| Computer: PC-compatible running Maple on MS Windows or Linux; SUN systems running Maple for Unix on OS Solaris. | ||
| Operating system: Windows 2000, Windows XP, Linux, Solaris. | ||
| RAM: below 100 Megabytes | ||
| Keywords: Symbolic computation, Lie Symmetry, Lie-Backlund symmetry, Higher symmetry, Approximate symmetry, Adjoint symmetry, Conservation law, Classification. | ||
| PACS: 02.30.Jr, 2.30.Hq, 02.20.Sv, 02.70.Wz. | ||
| Classification: 5. | ||
Nature of problem: Any physical model containing linear or nonlinear partial or ordinary differential equations. | ||
Solution method: Symbolic computation of Lie, higher and approximate symmetries by Lie's algorithm. Symbolic computation of conservation laws and adjoint symmetries by using multipliers and Euler operator properties. High performance is achieved by using an efficient representation of the system under consideration and resulting symmetry/conservation law determining equations: all dependent variables and derivatives are represented as symbols rather than functions or expressions. | ||
Restrictions: The GeM module routines are normally able to handle ODE/PDE systems of high orders (up to order seven and possibly higher), depending on the nature of the problem. Classification of symmetries/conservation laws with respect to one or more arbitrary constitutive function(s) of one or two arguments is normally accomplished successfully. | ||
Running time: 1 - 20 seconds for problems that do not involve classification; 5 - 1000 seconds for problems that involve classification, depending on complexity. | ||
References: | ||
| [1] | The updated versions of the GeM package and the documentation are available at http://www.math.ubc.ca/~alexch/gem/. | |
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