Some fast finite-difference solvers for Dirichlet problems on special domains

Ta Van Dinh

Aplikace matematiky (1982)

  • Volume: 27, Issue: 3, page 161-166
  • ISSN: 0862-7940

Abstract

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The author proves the existence of the multi-parameter asymptotic error expansion to the usual five-point difference scheme for Dirichlet problems for the linear and semilinear elliptic PDE on the so-called uniform and nearly uniform domains. This expansion leads, by Richardson extrapolation, to a simple process for accelerating the convergence of the method. A numerical example is given.

How to cite

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Dinh, Ta Van. "Some fast finite-difference solvers for Dirichlet problems on special domains." Aplikace matematiky 27.3 (1982): 161-166. <http://eudml.org/doc/15236>.

@article{Dinh1982,
abstract = {The author proves the existence of the multi-parameter asymptotic error expansion to the usual five-point difference scheme for Dirichlet problems for the linear and semilinear elliptic PDE on the so-called uniform and nearly uniform domains. This expansion leads, by Richardson extrapolation, to a simple process for accelerating the convergence of the method. A numerical example is given.},
author = {Dinh, Ta Van},
journal = {Aplikace matematiky},
keywords = {multi-parameter asymptotic error expansion; five-point difference scheme; Dirichlet problems; Richardson extrapolation; accelerating the convergence; numerical example; multi-parameter asymptotic error expansion; five-point difference scheme; Dirichlet problems; Richardson extrapolation; accelerating the convergence; numerical example},
language = {eng},
number = {3},
pages = {161-166},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some fast finite-difference solvers for Dirichlet problems on special domains},
url = {http://eudml.org/doc/15236},
volume = {27},
year = {1982},
}

TY - JOUR
AU - Dinh, Ta Van
TI - Some fast finite-difference solvers for Dirichlet problems on special domains
JO - Aplikace matematiky
PY - 1982
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 27
IS - 3
SP - 161
EP - 166
AB - The author proves the existence of the multi-parameter asymptotic error expansion to the usual five-point difference scheme for Dirichlet problems for the linear and semilinear elliptic PDE on the so-called uniform and nearly uniform domains. This expansion leads, by Richardson extrapolation, to a simple process for accelerating the convergence of the method. A numerical example is given.
LA - eng
KW - multi-parameter asymptotic error expansion; five-point difference scheme; Dirichlet problems; Richardson extrapolation; accelerating the convergence; numerical example; multi-parameter asymptotic error expansion; five-point difference scheme; Dirichlet problems; Richardson extrapolation; accelerating the convergence; numerical example
UR - http://eudml.org/doc/15236
ER -

References

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  1. O. V. Widlund, Some recent applications of asymptotic error expansions to finite difference schemes, Proc. Royal Soc. London, A 323, N. 1553 (1971), 167-177. (1971) Zbl0221.65005MR0495006

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