On multi-parameter error expansions in finite difference methods for linear Dirichlet problems
Dinh, Ta Van
Applications of Mathematics, Tome 32 (1987), p. 16-24 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 1987-01-01
Classification:  35J25,  65N06,  65N15 
@article{104232,
     author = {Ta Van Dinh},
     title = {On multi-parameter error expansions in finite difference methods for linear Dirichlet problems},
     journal = {Applications of Mathematics},
     volume = {32},
     year = {1987},
     pages = {16-24},
     zbl = {0629.65109},
     mrnumber = {0879326},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104232}
}

Dinh, Ta Van. On multi-parameter error expansions in finite difference methods for linear Dirichlet problems. Applications of Mathematics, Tome 32 (1987) pp. 16-24. http://gdmltest.u-ga.fr/item/104232/

Г. И. Марчук В. В. Шайдуров Повышение точности решений разностных схем, Москва, Наука, 1979. (1979) | Zbl 1225.01075

О. А. Ладыженская H. H. Уралъцева Линейные и квазилинейные уравнения эллиптического типа, Москва, Наука, 1973. (1973) | Zbl 1221.53041