An improved pseudospectral approximation of generalized Burger-Huxley and Fitzhugh-Nagumo equations

In this paper, an improved Chebyshev-Gauss-Lobatto pseudospectral approximation of nonlinear Burger-Huxley and Fitzhugh-Nagumo (FN) equations have been presented. The spectral method has been employed in time and space based upon Chebyshev Gauss-Labatto points and achieved spectral accuracy. A mapping has used to transform the initial-boundary value non-homogeneous problems to homogeneous problems and finally it reduced to a system of algebraic equations, which has solved by standard numerical method. Numerical results for various cases of generalized Burger-Huxley equation and other examples of Fitzhugh-Nagumo equation have presented to demonstrate the performance and effectiveness of the method. Comparison of the method with existing other methods, available in literature, are also given.