# On multi-parameter error expansions in finite difference methods for linear Dirichlet problems

Aplikace matematiky (1987)

- Volume: 32, Issue: 1, page 16-24
- ISSN: 0862-7940

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topDinh, Ta Van. "On multi-parameter error expansions in finite difference methods for linear Dirichlet problems." Aplikace matematiky 32.1 (1987): 16-24. <http://eudml.org/doc/15476>.

@article{Dinh1987,

abstract = {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.},

author = {Dinh, Ta Van},

journal = {Aplikace matematiky},

keywords = {error expansion; Dirichlet problem; selfadjoint; central difference scheme; finite difference method; error expansion; Dirichlet problem; selfadjoint; central difference scheme},

language = {eng},

number = {1},

pages = {16-24},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On multi-parameter error expansions in finite difference methods for linear Dirichlet problems},

url = {http://eudml.org/doc/15476},

volume = {32},

year = {1987},

}

TY - JOUR

AU - Dinh, Ta Van

TI - On multi-parameter error expansions in finite difference methods for linear Dirichlet problems

JO - Aplikace matematiky

PY - 1987

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 32

IS - 1

SP - 16

EP - 24

AB - 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.

LA - eng

KW - error expansion; Dirichlet problem; selfadjoint; central difference scheme; finite difference method; error expansion; Dirichlet problem; selfadjoint; central difference scheme

UR - http://eudml.org/doc/15476

ER -

## References

top- Г. И. Марчук В. В. Шайдуров, Повышение точности решений разностных схем, Москва, Наука, 1979. (1979) Zbl1225.01075
- О. А. Ладыженская H. H. Уралъцева, Линейные и квазилинейные уравнения эллиптического типа, Москва, Наука, 1973. (1973) Zbl1221.53041

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