Application of spectral collocation method to a class of nonlinear PDEs

In this paper approximate solutions to a class of nonlinear partial differential equations by means of the Chebyshev spectral collocation method is considered. First, properties of the Chebyshev spectral collocation method required for our subsequent development are given and utilized to reduce the computation of Fisherʹs, generalized Burgerʹs-Fisher, generalized Huxley, and generalized Burgerʹs-Huxley equations to some system of ordinary differential equations. Then, we use fourth-order Runge-Kutta formula for the numerical solution of the system of ordinary differential equations. The method is applied to a few test examples to illustrate the accuracy and the implementation of the method.