On comparing the accuracy of some finite difference methods for parabolic partial differential equations

Methods for comparing the accuracy of numerical methods for the solution of parabolic partial differential equations are briefly surveyed. Criteria for a more systematic comparison are proposed and applied to an accuracy comparison of the classical and the modified Saul'yev methods and the Crank–Nicholson method on a simple linear problem. The results obtained, which include observation of the existence of optimal spatial mesh size for the two Saul'yev methods, are discussed