In this paper a solution of combined field integral equation (CFIE) for electromagnetic scattering by an arbitrary shaped dielectric object is studied. We derive a novel CFIE formulation in which the electric and magnetic field integral equations (EFIE and MFIE) are combined in the usual manner outside the object. Inside the object CFIE is composed by changing the roles of EFIE and MFIE. In add...

In this paper, Bernstein piecewise polynomials are used to solve the integral equations numerically. A matrix formulation is given for a non-singular linear Fredholm Integral Equation by the technique of Galerkin method. In the Galerkin method, the Bernstein polynomials are exploited as the linear combination in the approximations as basis functions. Examples are considered to verify the effect...

We develop a numerical method based on Sine functions to obtain an approximate solution of a one-dimensional Cauchy singular integral equation (CSIE) over an arbitrary, smooth, open arc L of finite length in the complex plane. At the outset, we reduce the CSIE to a Fredholm integral equation of the second kind via a regularization procedure. We then obtain an approximate solution to the Fredhol...

In this paper, we studied the numerical solution of nonlinear weakly singular Volterra-Fredholm integral equations by using the product integration method. Also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear Volterra-Fredholm integral equations. The reliability and efficiency of the proposed scheme are...

in this article,we present a wavelet method for solving stochastic volterra integral equations based on haar wavelets. first, we approximate all functions involved in the problem by haar wavelets then, by substituting the obtained approximations in the problem, using the it^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation w...

In the present paper, the solution of a singular integral equation with logarithmic kernel in two disjoint intervals (0, a)4(b, ∞), (a, b are finite) is obtained by using function theoretic method. The two cases are considered when the unknown function satisfying the integral equation is unbounded or bounded at both nonzero finite end points of the interval. In the latter case, two solvability ...

The uniqueness of positive solution for a class of singular fractional differential system with integral boundary conditions is considered in this paper and many types of equation system are contained in this equation system because there are many parameters which can be changeable in this equation system. The fractional orders are involved in the nonlinearity of the boundary value problem and ...

We discuss a possibility to construct high order methods on uniform or mildly graded grids for the numerical solution of linear Volterra integro-differential equations with weakly singular or other nonsmooth kernels. Using an integral equation reformulation of the initial value problem, we apply to it a smoothing transformation so that the exact solution of the resulting equation does not conta...

We investigate the structure of the nonlocal closure relation in the kinetic equation for a soliton gas. This kinetic equation represents an integro-differential nonlinear system which has been recently shown to possess a number of remarkable properties and seems to be a representative of an entirely new class of integrable systems. In this paper, we identify the nonlocal kinetic closure relati...

A class of multi-wavelet bases for L2 is constructed with the property that a variety of integral operators is represented in these bases as sparse matrices, to high precision. In particular, an integral operator K whose kernel is smooth except along a nite number of singular bands has a sparse representation. In addition, the inverse operator (I K) 1 appearing in the solution of a second-kind ...