We present, in a uniform manner, several integral equations of the first kind for the solution of the two-dimensional interior Dirichlet boundary value problem. We apply a general numerical collocation method to the various equations, and thereby we compare the various integral equations, and recommend two of them. We give a survey of the various numerical methods, and present a simple method for the numerical solution of the recommended integral equations.
@article{104357,
author = {S\o ren Christiansen},
title = {First kind integral equations for the numerical solution of the plane Dirichlet problem},
journal = {Applications of Mathematics},
volume = {34},
year = {1989},
pages = {285-302},
zbl = {0695.65068},
mrnumber = {1008581},
language = {en},
url = {http://dml.mathdoc.fr/item/104357}
}
Christiansen, Søren. First kind integral equations for the numerical solution of the plane Dirichlet problem. Applications of Mathematics, Tome 34 (1989) pp. 285-302. http://gdmltest.u-ga.fr/item/104357/
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