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Application of semi-analytic methods for the Fitzhugh-Nagumo equation, which models the transmission of nerve impulses. (English) Zbl 1196.35025
Summary: The homotopy perturbation method (HPM), the variational iteration method (VIM) and the Adomian decomposition method (ADM) are applied to solve the Fitzhugh-Nagumo equation. Numerical solutions obtained by these methods when compared with the exact solutions reveal that the obtained solutions produce high accurate results. The results show that the HPM, the VIM and the ADM are of high accuracy and are efficient for solving the Fitzhugh-Nagumo equation. Also the results demonstrate that the introduced methods are powerful tools for solving the nonlinear partial differential equations.

MSC:
35A25 Other special methods applied to PDEs
35K57 Reaction-diffusion equations
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