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

Carasso, Alfred; Parter, Seymour V.

doi:10.1090/S0025-5718-1970-0284019-9

An analysis of “boundary-value techniques” for parabolic problems.
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by Alfred Carasso and Seymour V. Parter PDF

Math. Comp. 24 (1970), 315-340 Request permission

Abstract:

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 $t \to \infty$, 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.

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