in this paper, we present a method for solving the rst kind abel integral equation. in thismethod, the rst kind abel integral equation is transformed to the second kind volterraintegral equation with a continuous kernel and a smooth deriving term expressed by weaklysingular integrals. by using sidi's sinm - transformation and modied navot-simpson'sintegration rule, an algorithm for...

In this paper we investigate the solvability of an ill-posed two-dimensional Fred-holm integral equation of the rst kind which allows the solutions of distribution type. The problem is rst transformed into a well-posed diierential-integral equation using output least-squares approach with a regularization of bounded variations. A globally convergent iterative method is proposed and some numeric...

There has been little progress in the analysis of two-way diffusion in the last few decades due to the difficulties brought by the interface section similar to a free boundary condition. In this paper, however, the equivalent probability model is considered and the interface section is precisely described by an integral equation. The solution of two-way diffusion is then expressed in an integra...

An interface integral equation is presented for the elastostatic problem in a two-dimensional isotropic composite. The displacement is represented by a single layer force density on the component interfaces. In a simple numerical example involving hexagonal arrays of disks the force density is expanded in a Fourier series. This leads to an algorithm with superalgebraic convergence. The integral...

We present a new high-order integral algorithm for the solution of scattering problems by heterogeneous bodies under TE radiation. Here, a scatterer is represented by a (continuously or discontinuously) varying refractive index ( ) within a two-dimensional (2-D) bounded region; solutions of the associated Helmholtz equation under given incident fields are then obtained by high-order inversion o...

Using the fundamental solution of the heat equation, we give an expression of the solutions to two-dimensional initial-boundary value problems of the Navier-Stokes equations, where the vorticity is expressed in terms of a Poisson integral, a Newtonian potential, and a single layer potential. The density of the single layer potential is the solution to an integral equation of Volterra type along...

A two-dimensional nonlinear aerodynamics representation analysis is proposed for the investigation of inviscid flowfields of unsteady airfoils. Such problems are reduced to the solution of a nonlinear multidimensional singular integral equation as the source and vortex strength distributions are dependent on the history of these distributions on the NACA airfoil surface. A turbulent boundary la...

In this study, we present a direct method to solve nonlinear two-dimensional VolterraHammerestein integral equations in terms of twodimensional piecewise constant block-pulse functions (2D-PCBFs). Properties of these functions and operational matrix of integration together with the product operational matrix are presented and used to transform the integral equation to a matrix equation which co...