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On the convergence of a modified block SOR algorithm. (English) Zbl 0948.65108

The author investigates a vector iterative alternating directions difference scheme for solving a multidimensional Poisson equation, reduces the scheme to a modified block successive overrelaxation (SOR) algorithm, investigates the stability and convergence of the scheme, determines the optimal iterative parameters, and estimates the error.

MSC:

65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65F10 Iterative numerical methods for linear systems
65N15 Error bounds for boundary value problems involving PDEs
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