Local and spectral approximations of the time-dependent coefficient diffusion equations

In this study, we consider numerical solution of the time-dependent coefficient diffusion equations. First, a staggered finite difference method is applied to obtain a local approximation for the solution. By using barycentric rational spectral method we drive a system of ordinary differential equations which gives the approximate solution for the time-dependent coefficient diffusion equations. The stability of the staggered Crank-Nicolson is considered. Finally the numerical results from the local and spectral methods are compared.