In this paper, a homotopy perturbation method (HPM) and modified homotopy perturbation (MHPM) are proposed to solve singular integral equation with generalized Abel's kernel.

A semi-spectral Chebyshev method for solving numerically singular integral equations is presented and applied in the quarkonium bound-state problem in momentum space. The integrals containing both, logarithmic and Cauchy singular kernels, can be evaluated without subtractions by dedicated automatic quadratures. By introducing a Chebyshev mesh and using the Nystrom algorithm the singular integra...

Transverse magnetic (TM) scattering of an electromagnetic wave from a periodic dielectric diffraction grating can mathematically be described by a volume integral equation. This volume integral equation, however, in general fails to feature a weakly singular integral operator. Nevertheless, after a suitable periodization, the involved integral operator can be efficiently evaluated on trigonomet...

This paper is concerned with finding approximate solution for the singular integral equations. Relating the singular integrals to Cauchy principal-value integrals, we expand the kernel and the density function of singular integral equation by the sum of the chebyshev polynomials of the first, second, third and fourth kinds. Some numerical examples are presented to illustrate the accuracy and ef...

We analyze electromagnetic TM scattering from a diffraction grating consisting of a dielectric with possibly negative real part. The scattering problem can be reformulated as a strongly singular volume integral equation, a technique that attracts continuous interest in the engineering community, but rarely received rigorous theoretic treatment. In this paper, we provide (generalized) G̊arding es...

In a classical paper, E. R. Love considered a certain function defined by a singular integral which is harmonic outside a circular disk. Love's objective was to derive a simple integral equation whose solution leads to a useful formula for the capacitance of the condenser consisting of two parallel circular plates. We close a gap in Love's derivation by finding a new nonsingular representation ...

The subject of this paper is the formulation of boundary integral equations for firstand second-order shape sensitivities of boundary elastic fields in three-dimensional bodies. Here the direct differentiation approach is considered. It relies on the repeated application of the material derivative concept to the governing regularized (i.e. weakly singular) displacement boundary integral equatio...

The symmetry present in Green's functions is exploited to signi®cantly reduce the matrix assembly time for a Galerkin boundary integral analysis. A relatively simple modi®cation of the standard Galerkin implementation for computing the non-singular integrals yields a 20±30 per cent decrease in computation time. This faster Galerkin method is developed for both singular and hypersingular equatio...

Singular integral equation method is one of the most effective numerical methods solving a plane crack problem in fracture mechanics. Depending on the choice of the density function, very often a higher order of sigularity appears in the equation, and we need to give a proper meaning of the integration. In this article we address the Hadamard finite part integral and how it is used to solve the...