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Some modern methods of solving grid equations. (English. Russian original) Zbl 0535.65076
Sov. Math. 27, No. 7, 1-13 (1983); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1983, No. 7(254), 3-12 (1983).
Summary: At the present time, much attention is being given to the construction of methods of solving the discrete analogs of boundary-value problems for elliptic equations in grid domains of complicated structure, which are based on the application of economical direct methods for simpler problems in regular domains, and also iterative methods, which use an incomplete decomposition of a difference operator into factors. We give a survey of a number of methods for effectively solving difference equations, which have been investigated by the authors of the paper.

MSC:
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
65F05 Direct numerical methods for linear systems and matrix inversion
65F10 Iterative numerical methods for linear systems
35J25 Boundary value problems for second-order elliptic equations
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