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

In this paper, we consider numerical approximation of generalised Burgers–Fisher equation using the pseudo-spectral method. For the time discretization we apply Crank–Nicolson /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.