In this paper, we formulate mathematical foundations of applications boundary integral equations with strongly singular integrals understood in the sense finite Hadamard value to numerical solution certain boundary-value problems. We describe schemes for solving based on quadrature formulas and collocation method. Also, make references known results justification methods described paper.

in this work, a new iterative method is proposed for obtaining the approximate solution of a class of hammerstein type integral equations system. the main structure of this method is based on the richardson iterative method for solving an algebraic linear system of equations. some conditions for existence and unique solution of this type equations are imposed. convergence analysis and error bou...

Szabo's models of acoustic attenuation [Szabo, J. Acoust. Soc. Am. 96(1), 491-500 (1994)] comply well with the empirical frequency power law involving noninteger and odd-integer exponent coefficients while guaranteeing causality, but nevertheless encounter the troublesome issues of hypersingular improper integral and obscurity in implementing initial conditions. The purpose of this paper is to ...

We propose a new algorithm for solving Helmholtz equations in the exterior domain. The algorithm not only combines the advantages of implicit surface representation and the boundary integral method, but also provides a new way to compute a class of the so-called hypersingular integrals. The keys to the proposed algorithm are the derivation of the volume integrals which are equivalent to any giv...

In a previous paper a preconditioning strategy based on overlapping domain decomposition was applied to the Galerkin approximation of elliptic partial differential equations on the sphere. In this paper the methods are extended to more general pseudodifferential equations on the sphere, using as before spherical radial basis functions for the approximation space, and again preconditioning the i...