A direct algorithm for evaluating hypersingular integrals arising in a three-dimensional Galerkin boundary integral analysis is presented. The singular integrals are defined as limits to the boundary, and by integrating two of the four dimensions analytically, the coincident integral is shown to be divergent. However, the divergent terms can be explicitly calculated and shown to cancel with cor...

Integral equations are in which the unknown function is found to be inside integral sign. N. H. Abel used equation analyze relationship between kinetic energy and potential a falling object, expressed by two equations. This called Abel's equation. Furthermore, these developed produce generalizations further for each study aims explain of first second kind Abel’s equations, find solution The met...

We analyze well-posedness of a scattering problem of time-harmonic electromagnetic waves by periodic structures with sign-changing coefficients. Transmission problems for Maxwell’s equations with sign-changing coefficients in bounded domains have been recently studied by Bonnet-Ben Dhia and co-workers in the so-called T -coercivity framework. In this article we generalize such framework for per...

While an integration by parts formula for the bilinear form of hypersingular boundary integral operator transient heat equation in three spatial dimensions is available literature, a proof this seems to be missing. Moreover, contains term including time derivative fundamental solution equation, whose interpretation difficult at second glance. To fill these gaps, we provide rigorous general vers...