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Dinh, Ta Van
Some fast finite-difference solvers for Dirichlet problems on special domains. (English). Aplikace matematiky, vol. 27 (1982), issue 3, pp. 161-166
MSC: 35J25, 65N15, 65N20, 65N22 | MR 0657999 | Zbl 0485.65070 | DOI: 10.21136/AM.1982.103959
Keywords:
multi-parameter asymptotic error expansion; five-point difference scheme; Dirichlet problems; Richardson extrapolation; accelerating the convergence; numerical example
Summary:
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.
References:
[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. MR 0495006 | Zbl 0221.65005
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