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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 ...

The fuzzy differential and integral equations are important part of the fuzzy analysis theory. Park et al. [8] have considered the existence of solution of fuzzy integral equation in Banach space and Subrahmaniam and Sudarsanam [12] proved the existence of solution of fuzzy functional equations. An integral equation is called singular if either the range of integration is infinite or the kernel...

Microscale contact between two solid surfaces induced by the liquid-bridging force is studied in the present article. Attention is focused on the interaction between the size of the contact area and the magnitude of the liquid-bridging force. The liquid-bridging force is related to the contact size and the other parameters, such as the filling angle, the contact angles, and the surface tension ...

In this paper we establish Gauss-type quadrature formulas for weakly singular integrals. An application of the quadrature scheme is given to obtain numerical solutions of the weakly singular Fredholm integral equation of the second kind. We call this method a discrete product-integration method since the weights involved in the standard product-integration method are computed numerically.

Abstract An innovative and groundbreaking mathematical approach is proposed for the determination of the properties of reservoir materials, when oil reserves together with water are moving through porous media. Such problem seems to be very important for oil reservoir engineering. So, the above problem is reduced to the solution of a non-linear singular integral equation, which is numerically e...