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On the numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation. (English) Zbl 0791.65089

A quadrature method is described for the numerical solution of the logarithmic integral equation of the first kind arising from the single- layer approach to the Dirichlet problem for the two-dimensional Helmholtz equation in smooth domains. An error analysis is developed in a Sobolev space setting and fast convergence rates for smooth boundary data are proven.

MSC:

65N38 Boundary element methods for boundary value problems involving PDEs
65R20 Numerical methods for integral equations
65N15 Error bounds for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
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References:

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