A comparison of Crank-Nicolson and Chebyshev rational methods for numerically solving linear parabolic equations

Abstract

A numerical comparison of the Crank-Nicolson and Chebyshev rational method is presented for problems involving a specific class of linear parabolic differential equations. The numerical results indicate that the Chebyshev rational method possesses a significant computational advantage over the standard Crank-Nicolson finite difference method. Numerical results are also used to demonstrate the usefulness of the Chebyshev rational method for solving problems involving piecewise-constant, as a function of time, boundary conditions and/or source terms. In addition, an efficient computational procedure is outlined for the Chebyshev method.