Saul’yev and Group Explicit Methods

The Saul’yev methods for parabolic equations are implicit in form, but can be solved explicitly and are therefore interesting in connection with non-linear problems. Abdullah’s Group Explicit methods are parallel in nature and therefore interesting when using parallel computers. The  main objective of this paper is to study the accuracy of these methods. Using global error estimation we show that for all these methods the time step must be bounded by the square of the space step size to ensure a global error which can be estimated. As a curiosity we show that the two original Saul’yev methods in fact solve two different differential equations.