Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 68, Issue 4, Pages 1006-1015Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2006.12.001
Keywords
Fitzhugh-Nagumo equation; Lie group method; invertible mapping; method of lines
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In this paper we investigate mappings of the classical Fitzhugh-Nagumo equation to a generalized Fitzhugh-Nagumo equation. These mappings are invertible and transform the solutions of the classical Fitzhugh-Nagumo equation into solutions of the generalized Fitzhugh-Nagumo equation considered here. These mappings are found by considering the Lie point symmetries admitted by the classical Fitzhugh-Nagumo equation and the generalized Fitzhugh-Nagumo equation considered here. A particular example of a generalized Fitzhugh-Nagumo equation that satisfies the boundary conditions of the classical Fitzhugh-Nagumo equation is considered. Numerical solutions of the generalized Fitzhugh-Nagumo equation that do not satisfy the boundary conditions of the classical Fitzhugh-Nagumo equation are obtained by implementing the Method of Lines. (C) 2007 Elsevier Ltd. All rights reserved.
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