asymptotic error expansion; Peaceman-Rachford; Richardson extrapolation; accelerating the convergence; numerical example
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.
 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 0495006
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