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error expansion; Dirichlet problem; selfadjoint; central difference scheme; finite difference method
The paper is concerned with the finite difference approximation of the Dirichlet problem for a second order elliptic partial differential equation in an $n$-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 ($n$-dimensional) rectangular grid in the directions of the individual axes appear as parameters.
[1] Г. И. Марчук В. В. Шайдуров: Повышение точности решений разностных схем. Москва, Наука, 1979. Zbl 1225.01075
[2] О. А. Ладыженская H. H. Уралъцева: Линейные и квазилинейные уравнения эллиптического типа. Москва, Наука, 1973. Zbl 1221.53041
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