Geodesic
Some fast finite-difference solvers for Dirichlet problems on special domains
Applications of Mathematics, Tome 27 (1982) no. 3, pp. 161-166.

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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.
DOI : 10.21136/AM.1982.103959
Classification : 35J25, 65N15, 65N20, 65N22
Keywords: multi-parameter asymptotic error expansion; five-point difference scheme; Dirichlet problems; Richardson extrapolation; accelerating the convergence; numerical example 
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     title = {Some fast finite-difference solvers for {Dirichlet} problems on special domains},
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Dinh, Ta Van. Some fast finite-difference solvers for Dirichlet problems on special domains. Applications of Mathematics, Tome 27 (1982) no. 3, pp. 161-166. doi : 10.21136/AM.1982.103959. http://geodesic.mathdoc.fr/articles/10.21136/AM.1982.103959/

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