Two methods for computing numerical conformai mappings are compared. The first, due to Symm, uses a Fredholm integral equation of the first kind while the other, due to Lichtenstein, uses a Fredholm integral equation of the second kind. The two methods are tested on ellipses with different ratios of major to minor axes. The method based on the integral equation of the second kind is superior if...

Three-body resonances in atomic systems are calculated as complexenergy solutions of Faddeev-type integral equations. The homogeneous FaddeevMerkuriev integral equations are solved by approximating the potential terms in a Coulomb-Sturmian basis. The Coulomb-Sturmian matrix elements of the three-body Coulomb Green’s operator has been calculated as a contour integral of two-body Coulomb Green’s ...

The contact problem of elastic bodies, each consisting of a finite layer of uniform thickness rigidly adhering to a half-plane, is investigated on the basis of the two-dimensional theory of elasticity. The materials of the layer and the half-plane in the contact body are isotropic and homogeneous, yet each of them may have distinct elastic properties. The mixed boundary value problem is reduced...

Droplets on insulating material suffer a nonvanishing total ponderomotive force because of the inhomogeneity of the surrounding electric field. A series expansion of this total force is proven in a two-dimensional setting by determining the line charge density at the boundary of the test body via a Fredholm integral equation, which is solved by Fourier techniques. The influence of electric char...

In this work we consider the numerical solution of a radiative transfer equation for modeling the emission of photons in stellar atmospheres. Mathematically, the problem is formulated in terms of a weakly singular Fredholm integral equation defined on a Banach space. Computational approaches to solve the problem are discussed, using direct and iterative strategies that are implemented in open s...

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...

In this paper, a numerical method for solving fuzzy Fredholm integral equations of the second kind is introduced. We apply the trapezoidal rule to compute the Riemann integrals.This kind of integral equations convert to a linear system. Then, by solving the linear system , unknowns are determined. Finally, an algorithm is presented to solve the fuzzy integral equation by using the trapezoidal r...