On multi-parameter error expansions in finite difference methods for linear Dirichlet problems
Ta Van Dinh (1987)
Aplikace matematiky
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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...