Geodesic
First kind integral equations for the numerical solution of the plane Dirichlet problem
Applications of Mathematics, Tome 34 (1989) no. 4, pp. 285-302.

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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.
DOI : 10.21136/AM.1989.104357
Classification : 35C15, 35J25, 45E10, 65N35, 65R20
Keywords: boundary integral equation; interior Dirichlet boundary value problem; Laplace equation; collocation method 
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Christiansen, Søren. First kind integral equations for the numerical solution of the plane Dirichlet problem. Applications of Mathematics, Tome 34 (1989) no. 4, pp. 285-302. doi : 10.21136/AM.1989.104357. http://geodesic.mathdoc.fr/articles/10.21136/AM.1989.104357/

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