Error Analysis of Chebyshev-Legendre Pseudo-spectral Method for a Class of Nonclassical Parabolic Equation

Many physical phenomena are modeled by nonclassical parabolic initial boundary value problems which involve a nonclassical term u xxt in the governed equation. Combining with the Crank-Nicolson/leapfrog scheme in time discretization, Chebyshev-Legendre pseudo-spectral method is applied to space discretization for numerically solving the nonclassical parabolic equation. The proposed approach is based on Legendre Galerkin formulation while the Chebyshev-Gauss-Lobatto (CGL) nodes are used in the computation. By using the proposed method, the computational complexity is reduced and both accuracy and efficiency are achieved. The stability and convergence are rigorously set up. The convergence rate shows ‘spectral accuracy’. Numerical experiments are presented to demonstrate the effectiveness of the method and to confirm the theoretical results.