Two-dimensional integral equations of the first kind over a circular disc are considered. The kernels involve the distance between two points on the disc raised to an arbitrary power. A review is given, comparing several published exact solutions for weakly-singular equations: these solutions are complicated, but three of them are shown to be equivalent. Some extensions to hypersingular equatio...

This paper develops a modification of the dressing method based on inhomogeneous linear integral equation with integral operator having nonempty kernel. Method allows one to construct the systems of multidimensional Partial Differential Equations (PDEs) having differential polynomial structure in any dimension n. Associated solution space is not full, although it is parametrized by certain numb...

a numerical method for solving nonlinear fredholm-volterra integral equations of general type is presented. this method is based on replacement of unknown function by truncated series of well known chebyshev expansion of functions. the quadrature formulas which we use to calculate integral terms have been imated by fast fourier transform (fft). this is a grate advantage of this method which has...

We discuss the numerical solution of a class of second-kind integral equations in which the integral operator is not compact. Such equations arise, for example, when boundary integral methods are applied to potential problems in a two-dimensional domain with corners in the boundary. We are able to prove the optimal orders of convergence for the usual collocation and product integration methods ...

on the basis of the steady-state two-dimensional theory of thermoelasticity, stress field around various holes in infinite isotropic plate is discussed. the plate is subjected to uniform heat flux and thermal insulated condition along the hole boundary is assumed. by using the complex potential functions and by applying the conformal mapping and solving the integral equations, the effect of blu...

Two sparse preconditioned iterative methods are presented to solve dense linear systems arising in the solution of two dimensional boundary integral equations. In the rst method, the sparse preconditioner is constructedsimply by choosing a small block of elements in the coeecient matrix of a dense linear system. The two-grid method falls into this category when the dense linear system arises fr...

In this article, we consider systems of integral-algebraic and integro-differential equations with weakly singular kernels. In the first part, we deal with two-dimensional integralalgebraic equations. Next, we analyze Volterra integral equations of the first kind with a degenerate matrix-kernel on the diagonal. Finally, the third part of the work is devoted to the analysis of degenerate integro...

In this paper, we use the continuous Legendre wavelets on the interval [0,1] constructed by Razzaghi M. and Yousefi S. [6] to solve the linear second kind integral equations. We use quadrature formula for the calculation of the products of any functions, which are required in the approximation for the integral equations. Then we reduced the integral equation to the solution of linear algebraic ...

A volume-surface integral equation (VSIE) formulation is developed for determining the electromagnetic TM scattering by a two-dimensional conducting cylinder coated with an inhomogeneous dielectric/magnetic material. The electric field integral equations (EFIEs) are utilized to derive the VSIE. The surface EFIE is applied to the conducting surface, while the volume EFIE is applied to the coatin...