Forward-Backward Saul'yev Method to Solve PDEs

In this paper we consider solidification of some parts, specially a large heavy roller. We use Saul'yev A and B methods simultaneously, for the first time, to solve the corresponding PDE, instead of standard explicit method. The object of the work was to reduce running time. Numerical experiments show that, in practice, using a large value for time step in Saul'yev forward-backward method not only reduce the running time considerably but also produces a more reliable method to solve this sort of problems. Also we show the truncation error of forwards-backward method is better than ordinary Saul'yev methods.

Heat equation, explicit method, Saul'yev methods, time step