### Abstract

Highly accurate finite difference schemes are developed for Laplace's equation with the Dirichlet boundary condition on general bounded regions in Rn. 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 0(h) in ¿j. 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.

Original language | English (US) |
---|---|

Pages (from-to) | 1-16 |

Number of pages | 16 |

Journal | Mathematics of Computation |

Volume | 31 |

Issue number | 137 |

DOIs | |

State | Published - 1977 |

### Fingerprint

### ASJC Scopus subject areas

- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics

### Cite this

*Mathematics of Computation*,

*31*(137), 1-16. https://doi.org/10.1090/S0025-5718-1977-0431736-X

**High order fast laplace solvers for the dirichlet problem on general regions.** / Pereyra, Victor; Proskurowski, Wtodzimierz; Widlund, Olof.

Research output: Contribution to journal › Article

*Mathematics of Computation*, vol. 31, no. 137, pp. 1-16. https://doi.org/10.1090/S0025-5718-1977-0431736-X

}

TY - JOUR

T1 - High order fast laplace solvers for the dirichlet problem on general regions

AU - Pereyra, Victor

AU - Proskurowski, Wtodzimierz

AU - Widlund, Olof

PY - 1977

Y1 - 1977

N2 - Highly accurate finite difference schemes are developed for Laplace's equation with the Dirichlet boundary condition on general bounded regions in Rn. 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 0(h) in ¿j. 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.

AB - Highly accurate finite difference schemes are developed for Laplace's equation with the Dirichlet boundary condition on general bounded regions in Rn. 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 0(h) in ¿j. 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.

UR - http://www.scopus.com/inward/record.url?scp=84966241274&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966241274&partnerID=8YFLogxK

U2 - 10.1090/S0025-5718-1977-0431736-X

DO - 10.1090/S0025-5718-1977-0431736-X

M3 - Article

VL - 31

SP - 1

EP - 16

JO - Mathematics of Computation

JF - Mathematics of Computation

SN - 0025-5718

IS - 137

ER -