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A finite difference domain decomposition algorithm for numerical solution of the heat equation. (English) Zbl 0732.65091

The authors give a finite difference method utilizing domain decomposition to allow one to divide the work of solving a heat equation. This method uses non-overlapping subdomains and is noniterative and is, thus, different from earlier methods. A purpose of this work is to introduce and analyze a fairly simple algorithm in 1- and 2-dimensional physical spaces. Attention is confined to intervals and squares, and maximum norm error estimates are given.
Interesting results are obtained and further extensions are pointed out.
Reviewer: V.P.Tyagi (Bombay)

MSC:

65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
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