A numerical solution of the generalized Burgers-Huxley equation by spectral collocation method. (English) Zbl 1100.65081

Summary: We present a new method for solving of the generalized Burgers-Huxley equation by using the collocation formula for calculating the spectral differentiation matrix for the Chebyshev-Gauss-Lobatto points. Firstly, the theory of application of pseudospectral method on the Burgers-Huxley equation presented. This method yields the Burgers-Huxley equation to a system of ordinary differential equations (ODEs). Secondly, we use the fourth-order Runge-Kutta formula for the numerical integration of the system of ODE. The numerical results obtained by this way are compared with the exact solution to show the efficiency of the method.


65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations


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