Chebyshev-Legendre pseudo-spectral method for the generalised Burgers-Fisher equation

摘要

In this paper, we consider numerical approximation of generalised Burgers-Fisher equation using the pseudo-spectral method. For the time discretization we apply Crank-Nicol-son /leapfrog scheme. The space discretization is based on Legendre Galerkin formulation while the Chebyshev-Gauss-Lobatto (CGL) nodes are used in practical computation, which is called "Chebyshev-Legendre" method. The stability and convergence are rigorously set up. Numerical experiments are presented to demonstrate the effectiveness of the method and to confirm the theoretical results.