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.
The author proves the existence of the multi-parameter asymptotic error expansion to the five-point difference scheme for Dirichlet problems for the linear and semilinear elliptic PDE on general domains. By Richardson extrapolation, this expansion leads to a simple process for accelerating the convergence of the method.
The paper is concerned with the finite difference approximation of the Dirichlet problem for a second order elliptic partial differential equation in an -dimensional domain. Considering the simplest finite difference scheme and assuming a sufficient smoothness of the domain, coefficients of the equation, right-hand part, and boundary condition, the author develops a general error expansion formula in which the mesh sizes of an (-dimensional) rectangular grid in the directions of the individual...
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.
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