Theses and Dissertations - UTB/UTPA
Date of Award
5-2012
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematics
First Advisor
Dr. Zhaosheng Feng
Second Advisor
Dr. Andras Balogh
Third Advisor
Dr. Paul Bracken
Abstract
There are many well-known techniques for obtaining exact solutions of differential equations, but some of them only work for a very limited class of problems and are merely special cases of a few power symmetry methods. These approaches can be applied to nonlinear differential of unfamiliar type; they do not rely on special “tricks." Instead, a given differential equation can be made to reveal its symmetries, which are then used to construct exact solutions. In this thesis, we briefly present the theory of the Lie symmetry method for finding exact solutions of nonlinear differential equations, then apply it to the study of the generalized Burgers-Huxley equation. Through analyzing the linearized symmetry condition and the associated determining system, we find two nontrivial infinitesimal generators, and obtain exact solutions by solving the reduced differential equation under certain parametric conditions. An approximate solution of the generalized Burgers-Huxley equation is established by means of the Adomian decomposition method.
Granting Institution
University of Texas-Pan American
Comments
Copyright 2012 Jing Tian. All Rights Reserved.
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