The boundary value problem for the Laplace equation outside several cracks in a plane is studied. The jump of the solution of the Laplace equation and the boundary condition containing the jump of its normal derivative are specified on the cracks. The problem has unique classical solution under certain conditions. The new integral representation for the unique solution of this problem is obtain...

In this paper a linear Fuzzy Fredholm Integral Equation(FFIE) with arbitrary Fuzzy Function input and symmetric triangular (Fuzzy Interval) output is considered. For each variable, output is the nearest triangular fuzzy number (fuzzy interval) to the exact fuzzy solution of (FFIE).

In this work we consider the rendering equation derived from the illumination model called Cook-Torrance model. A Monte Carlo (MC) estimator for numerical treatment of the this equation, which is the Fredholm integral equation of second kind, is constructed and studied.

Recursively Compressed Inverse Preconditioning (RCIP) is a numerical method for solving Fredholm second kind boundary integral equations in situations where the boundary shape induces a non-smooth behavior in the solution. The method originated in 2008 within a scheme for Laplace’s equation in two-dimensional domains with corners. In a series of subsequent papers the method was then refined and...

There are many ways to solve potential problems for anisotropic mixtures. The nite element method is a popular choice with great exibility that gives the solution in the entire computational domain. EEective medium approximation is a simpler option that only estimates eeective properties. Interface integral equation methods is a third class of methods that has been studied for a long time, but ...

in this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear volterra integral equations of the first-kind is proposed. this problem is transformedto a nonlinear two-dimensional volterra integral equation of the second-kind. the properties ofthe bivariate shifted legendre functions are presented. the operational matrices of integrationtogether with the produ...

Recently, Wazwaz has studied the regularization method to one-dimensional linear Fredholm integral equations of first kind [Wazwaz, 2011]. In this work, we develop for and nonlinear two-dimensional Fred-holm kind. Indeed, is used directly. But are transformed linearintegral by a change variable; then, The Regularization-Homotopy Method applied. combination homotopy perturbation method, or short...

We analyze well-posedness of a scattering problem of time-harmonic electromagnetic waves by periodic structures with sign-changing coefficients. Transmission problems for Maxwell’s equations with sign-changing coefficients in bounded domains have been recently studied by Bonnet-Ben Dhia and co-workers in the so-called T -coercivity framework. In this article we generalize such framework for per...

Since various problems in science and engineering fields can be modeled by nonlinear Volterra-Fredholm integral equations, the main focus of this study is to present an effective numerical method for solving them. This method is based on the hybrid functions of Legendre polynomials and block-pulse functions. By using this approach, a nonlinear Volterra-Fredholm integral equation reduces to a no...