High order fast Laplace solvers for the Dirichlet problem on general regions

Authors:
Victor Pereyra, Wlodzimierz Proskurowski and Olof Widlund

Journal:
Math. Comp. **31** (1977), 1-16

MSC:
Primary 65N15; Secondary 65B05

DOI:
https://doi.org/10.1090/S0025-5718-1977-0431736-X

MathSciNet review:
0431736

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Abstract: Highly accurate finite difference schemes are developed for Laplace's equation with the Dirichlet boundary condition on general bounded regions in . A second order accurate scheme is combined with a deferred correction or Richardson extrapolation method to increase the accuracy. The Dirichlet condition is approximated by a method suggested by Heinz-Otto Kreiss. A convergence proof of his, previously not published, is given which shows that, for the interval size *h*, one of the methods has an accuracy of at least in . The linear systems of algebraic equations are solved by a capacitance matrix method. The results of our numerical experiments show that highly accurate solutions are obtained with only a slight additional use of computer time when compared to the results obtained by second order accurate methods.

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DOI:
https://doi.org/10.1090/S0025-5718-1977-0431736-X

Article copyright:
© Copyright 1977
American Mathematical Society