Theses and Dissertations - UTB/UTPA
Date of Award
Master of Science (MS)
Dr. Zhaosheng Feng
Dr. Andras Balogh
Dr. Paul Bracken
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.
University of Texas-Pan American
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