Geodesic
On multi-parameter error expansions in finite difference methods for linear Dirichlet problems
Applications of Mathematics, Tome 32 (1987) no. 1, pp. 16-24

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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 $n$-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.
DOI : 10.21136/AM.1987.104232
Classification : 35J25, 65N06, 65N15
Keywords: error expansion; Dirichlet problem; selfadjoint; central difference scheme; finite difference method 
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     title = {On multi-parameter error expansions in finite difference methods for linear {Dirichlet} problems},
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Dinh, Ta Van. On multi-parameter error expansions in finite difference methods for linear Dirichlet problems. Applications of Mathematics, Tome 32 (1987) no. 1, pp. 16-24. doi: 10.21136/AM.1987.104232

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