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Domain-imbedding alternating direction method for linear elliptic equations on irregular regions using collocation. (English) Zbl 0764.65069
Author’s summary: A new method is presented for solving elliptic partial differential equations over two-dimensional irregular regions. The scheme imbeds the irregular region in a rectangle, and then uses an alternating direction iteration to solve the resulting system of linear equations.
Collocation with cubic Hermite splines is used for discretization. The method is shown to be equivalent to a multiboundary alternating direction method. A theory of convergence for a simplified case is given, details of implementation are discussed, and two numerical illustrations are presented.

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65F10 Iterative numerical methods for linear systems
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