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A Nyström method for boundary integral equations in domains with corners. (English) Zbl 0707.65078

The core of this work is a high order quadrature formula for integrals with endpoint singularities. The author obtains such a formula using the trapezoidal rule for the transformed integral. This quadrature rule is then applied in the Nyström method for a class of integral equations of the second kind with endpoint singularities. Finally, the method is applied to the boundary integral equations of the plane potential theory in domains with corners.
Reviewer: C.I.Gheorghiu

MSC:

65N38 Boundary element methods for boundary value problems involving PDEs
65R20 Numerical methods for integral equations
65D32 Numerical quadrature and cubature formulas
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
31A25 Boundary value and inverse problems for harmonic functions in two dimensions
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References:

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