Symbolic software for symmetry reduction and computation of invariant solutions of differential equations

Problems involving partial or ordinary differential equations arise in various fields of science. Therefore, the task of obtaining exact solutions of differential equations is of primary importance, and attracts high attention. The main purpose of the current thesis is the development of a Maple-based, symbolic software package for symmetry reduction of differential equations and computation of symmetry-invariant solutions. The package developed in the current thesis is compatible with and can be viewed as an extension of the package GeM for symbolic symmetry analysis, developed by Prof. Alexei Cheviakov. The reduction procedure is based on the Lie's classical symmetry reduction method involving canonical coordinates. The developed package is applicable for obtaining solutions arising from extension of Lie's method, in particular, nonlocal and approximate symmetries. The developed software is applied to a number of PDE problems to obtain exact invariant solutions. The considered equations include the one-dimensional nonlinear heat equation, the potential Burgers' equation, as well as equations arising in nonlinear elastostatics and elastodynamics.

Name thesis:degree_name

Master of Science (M.Sc.)

Level thesis:degree_level

Masters

Discipline thesis:degree_discipline

Mathematics and Statistics

Grantor

University of Saskatchewan

Year dc:date.issued

2011

Author dc:creator

• Olinov, Andrey I.

Advisor dc:contributor.advisor

• Cheviakov, Alexei F.

Committee members dc:contributor.committeemember

• Bikis, Miķelis G.
• Szmigielski, Jacek
• Koustov, Sasha

• Invariant solutions
• Symmetry reduction

Language dc:language.iso

en_US

Handle dc:identifier.uri

https://hdl.handle.net/10388/etd-05312011-142943

OAI identifier oai:identifier

oai:harvest.usask.ca:10388/etd-05312011-142943