Alternating direction implicit methods for two-dimensional diffusion with a non-local boundary condition. (English) Zbl 0949.65085
An initial-boundary value problem for the two-dimensional heat equation with non-local boundary conditions containing an unknown function is considered. A solution technique based on the second-order ADI method of D. W. Peaceman and H. H. Rachford jun. and its fourth-order modification of A. Mitchell and Fairweather [Numer. Math. 6, 285-292 (1964; Zbl 0123.12001)] is described. Comparisons with a fully-implicit scheme are presented.
Reviewer: A.I.Tolstykh (Moskva)
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35K05 | Heat equation |
| 65F10 | Iterative numerical methods for linear systems |
Keywords:
heat equation; non-local boundary condition; ADI methods; alternating direction implicit methods; diffusion equationReferences:
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