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Mathematics of Computation

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An analysis of ``boundary-value techniques'' for parabolic problems.

Authors: Alfred Carasso and Seymour V. Parter
Journal: Math. Comp. 24 (1970), 315-340
MSC: Primary 65.68
MathSciNet review: 0284019
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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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Keywords: Boundary-value technique, parabolic equations, use of limiting steady-state, long times
Article copyright: © Copyright 1970 American Mathematical Society