An accurate double Chebyshev spectral approximation for parabolic partial differential equations (Q1374091)

Spectral methods based on double Chebyshev expansion for solving numerically partial differential equations have been used by many authors. In this paper two alternative methods are developed, which reduce a parabolic partial differential equation in two space variables in a square subjected to the most general inhomogeneous mixed boundary and initial conditions to a system of ordinary differential equations in the spectral Chebyshev expansion coefficients. This system is greatly simplified by using the Kronecker matrix algebra and it is solved by the step-by-step method. Numerical results show that both methods compare favourably with the theoretical solution.