in this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the laplacian equation. themethod is based on the use of the galerkin method with cas wavelets constructed on the unit interval as basis.this approach utilizes the non-uniform gauss-legendre quadrature rule for ...

In this work, we explain a new numerical schemes of collocation methods based on the adapted quadratic approximation of singular integral with logarithmic kernel. This approximation leads to obtain the numerical solution of singular integral equations with logarithmic kernel on an oriented smooth contour.

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...

A universal approach by Laplace transform to the variational iteration method for fractional derivatives with the nonsingular kernel is presented; in particular, the Caputo-Fabrizio fractional derivative and the Atangana-Baleanu fractional derivative with the non-singular kernel is considered. The analysis elaborated for both non-singular kernel derivatives is shown the necessity of considering...

A direct function theoretic method is applied to solve a weakly singular integral equation whose kernel involves logarithmic singularity. This method avoids the occurrence of strong singularity. The solution of this integral equation is then applied to re-investigate the well known problem of water wave scattering by a partially immersed vertical barrier. c © 2008 Published by Elsevier Ltd

The current on a linear strip or wire solves an equation governed by a linear integraldifferential operator that is the composition of the Helmholtz operator and an integral operator with logarithmically singular displacement kernel. We investigate the spectral behavior of this classical operator, particularly because various methods of analysis and solution rely on asymptotic properties of spe...

In this article we analyze the resolvent, the heat kernel and the spectral zeta function of the operator −d/dr−1/(4r) over the finite interval. The structural properties of these spectral functions depend strongly on the chosen self-adjoint extension of the operator, a choice being made necessary because of the singular potential present. Only for the Friedrichs extension standard properties ar...

We used function theoretic method to solve a singular integral equation with logarithmic kernel in two disjoint finite intervals where the unknown function satisfying the integral equation may be bounded or unbounded at the nonzero finite endpoints of the interval concerned. An appropriate solution of this integral equation is then applied to solve the problem of scattering of time harmonic sur...

In this work, we evaluate the conditionally positive definite logarithmic kernel in kernel-based estimation of reflectance spectra. Reflectance spectra are estimated from responses of a 12-channel multispectral imaging system. We demonstrate the performance of the logarithmic kernel in comparison with the linear and Gaussian kernel using simulated and measured camera responses for the Pantone a...

A simple method for solving Prandtl's integro-differential equation is proposed based on a new reproducing kernel space. Using a transformation and modifying the traditional reproducing kernel method, the singular term is removed and the analytical representation of the exact solution is obtained in the form of series in the new reproducing kernel space. Compared with known investigations, its ...