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ADI method – domain decomposition. (English) Zbl 1099.65084
A domain decomposition algorithm which is based on an implicit prediction and fully implicit scheme for the interior values, for solving parabolic partial differential equations, is presented. It is shown that this algorithm without the correction procedure is unconditionally stable. The modified alternating direction implicit (ADI) algorithm is deduced from this algorithm so that the ADI method is considered as the extreme case of the domain decomposition algorithm.

65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
Full Text: DOI
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