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...

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...

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...

In this paper, an iterative scheme for extracting approximate solutions of two dimensional Volterra-Fredholm integral equations is proposed. Considering some conditions on the kernel of the integral equation obtained by discretization of the integral equation, the convergence of the approximate solution to the exact solution is investigated. Several examples are provided to demonstrate the effi...

The problem of excitation of electromagnetic fields by a material body of finite dimensions in presence of coupling hole between two arbitrary electrodynamic volumes is formulated. The problem is reduced to two-dimensional integral equations for the surface electric current on a material body and the equivalent magnetic current on a coupling hole. A physically correct transition from the initia...

The mean exit time and escape probability are deterministic quantities that can quantify dynamical behaviors of stochastic differential equations with non-Gaussian α-stable type Lévy motions. Both deterministic quantities are characterized by differential-integral equations (i.e., differential equations with nonlocal terms) but with different exterior conditions. A convergent numerical scheme i...

in this paper, we will compare a homotopy perturbation algorithm and taylor series expansin method for a system of second kind fredholm integral equations. an application of he’s homotopy perturbation method is applied to solve the system of fredholm integral equations. taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation.

an ecient method, based on the legendre wavelets, is proposed to solve thesecond kind fredholm and volterra integral equations of hammerstein type.the properties of legendre wavelet family are utilized to reduce a nonlinearintegral equation to a system of nonlinear algebraic equations, which is easilyhandled with the well-known newton's method. examples assuring eciencyof the method and ...

this paper gives an ecient numerical method for solving the nonlinear systemof volterra-fredholm integral equations. a legendre-spectral method based onthe legendre integration gauss points and lagrange interpolation is proposedto convert the nonlinear integral equations to a nonlinear system of equationswhere the solution leads to the values of unknown functions at collocationpoints.