ABSTRACT
However, explicit methods share one undesirable feature: they are only conditionally stable. Consequently, the allowable time step is usually quite small, and the amount of computational effort required to obtain the solution of some problems is immense. A procedure for avoiding the time step limitation would obviously be desirable. Implicit finite difference methods furnish such a procedure. Implicit finite difference methods are unconditionally stable. There is no limit on the allowable time step required to achieve a stable solution. There is, of course, some practical limit on the time step required to maintain the truncation errors within reasonable limits, but this is not a stability consideration; it is an accuracy consideration.
