The computation schemes of spline-collocation methods for solving singular integral equations. A theoretical foundation of these two methods is obtained in space L2. In the present paper we give theoreticaly justification of the numerical schemes of spline-collocation method for solving the singular integral equations (SIE) of the following form

The paper presents an exact solution to the internal boundary value problem of field distribution in electrostatic lens formed by two identical semi-infinite coaxially located round cylinders separated a slit finite width and inside infinite outer cylinder. is reduced system singular Wiener–Hopf integral equations, which further solved method using factorized Bessel functions. Solutions for eac...

In this article , we prove some new theorems related to l 2-transform defined in [1],[2],[3] .We also give an application for solution to Fox singular integral equations with trigonometric kernel and the non-homogeneous systems of differential equations.

In present paper we elaborated the numerical schemes of iterative methods for an approximate solution of weak singular integral equations with logarithmic Kernel. The equation is examined in a pair of spaces. The results obtained could be used for any pair of the functional spaces where the problem of finding the solution of weak singular integral equations is correctly formulated problem by Ti...

in this paper, a nonlinear volterra-fredholm integral equation of the first kind is solved by using the homotopy analysis method (ham). in this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by ham. the approximate solution of this equation is calculated in the form of a series which its components are computed easily. the accuracy...

In this paper, we present a computational method for solving boundary integral equations with logarithmic singular kernels which occur as reformulations of a boundary value problem for Laplace’s equation. The method is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis. This approach utilizes the nonuniform Gauss-Legendre quadrature rule for appr...