Geodesic
Some fast finite-difference solvers for two-dimensional evolutionary equations on special domains
Applications of Mathematics, Tome 27 (1982) no. 5, pp. 313-318
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The author proves the existence of the asymptotic error expansion to the Peaceman-Rachford finite-difference scheme for the first boundary value problem of the two-dimensional evolationary equation 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.
The author proves the existence of the asymptotic error expansion to the Peaceman-Rachford finite-difference scheme for the first boundary value problem of the two-dimensional evolationary equation 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.1982.103978
Classification : 35G10, 35K25, 65M15, 65N12, 65N15
Keywords: asymptotic error expansion; Peaceman-Rachford; Richardson extrapolation; accelerating the convergence; numerical example 
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     title = {Some fast finite-difference solvers for two-dimensional evolutionary equations on special domains},
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Dinh, Ta Van. Some fast finite-difference solvers for two-dimensional evolutionary equations on special domains. Applications of Mathematics, Tome 27 (1982) no. 5, pp. 313-318. doi: 10.21136/AM.1982.103978

[1] O. B. Widlund: Some recent applications of asymptotic error expansions to finite difference schemes. Proc. Roy. Soc. London, A 323, N. 1553, 1971, 167-177. | MR | Zbl

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