ABSTRACT
The apparent stability restriction, d .::: 0.5, imposes a serious limitation on the usefulness of the FTCS method for solving the diffusion equation. One procedure for deciding whether or not a solution is accurate enough is to cut Ax in half and repeat the solution up to the same specified time level to see if the solution changes significantly. For the FTCS method, cutting Ax in half while holding d constant requires a factor of four decreases in !1t. Thus, four times as many time steps are required to reach the previously specified time level, and twice as much work is required for each time step since twice as many physical grid points are involved. Thus, the total computational effort increases by a factor of 8!
