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Finite-difference methods for parabolic initial boundary problems are usually treated as marching procedures. However, if the solution reaches a known steady state value as t - , one may provide approximate values on a line t = T for a preselected T suitably large. With this extra data, it is feasible to consider the use of elliptic boundary-value techniques for the numerical computation of such problems. In this report we give a complete analysis of this method for the linear second-order case with time-independent coefficients. We also discuss iterative methods for solving the difference equations. Finally, we give an example where the method fails.

An analysis of “boundary-value techniques” for parabolic problems.