We develop a simple, efficient numerical method of boundary integral type for solving an elliptic partial differential equation in a three-dimensional region using the classical formulation of potential theory. Accurate values can be found near the boundary using special corrections to a standard quadrature. We treat the Dirichlet problem for a harmonic function with a prescribed boundary value...

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...

We propose a nonlinear integral equation (NLIE) with only one unknown function, which gives the free energy of the integrable one dimensional Heisenberg model with arbitrary spin. In deriving the NLIE, the quantum Jacobi-Trudi and Giambelli formula (BazhanovReshetikhin formula), which gives the solution of the T -system, plays an important role. In addition, we also calculate the high temperatu...

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...

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...