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...

In this paper, we introduce an approach by using inverse fuzzy transforms based on the fuzzy partition with combination in collocation technique for the numerical solution of Fredholm integral equations of the second kind. The main advantage of this approach is to reduce the problem to the linear system of equations. We present the convergence theorem for this method. Finally, we give two examp...

This paper gives a regular vector boundary integral equation for solving the problem of viscous scattering of a pressure wave by a rigid body. Firstly, single-layer viscous potentials and a generalized stress tensor are introduced. Correspondingly, generalized viscous double-layer potentials are defined. By representing the scattered field as a combination of a single-layer viscous potential an...

Fuzzy differential and integral equations have been studied by many authors [1, 2, 5, 6, 7, 14]. Kaleva [5] discussed the properties of differentiable fuzzy set-valued mappings by means of the concept of H-differentiability introduced by Puri and Ralescu [9]. Seikkala [11] defined the fuzzy derivative which is a generalization of the Hukuhara derivative [9] and the fuzzy integral which is the s...

The asymmetric problem of rocking rotation of a circular rigid disk embedded in a finite depth of a transversely isotropic half-space is analytically addressed. The rigid disk is assumed to be in frictionless contact with the elastic half-space. By virtue of appropriate Green's functions, the mixed boundary value problem is written as a dual integral equation. Employing further mathematical tec...

We consider nonlinear integral equations of Fredholm and Volterra type with respect to functions having values in L-spaces. Such class of equations includes set-valued integral equations, fuzzy integral equations and many others. We prove theorems of existence and uniqueness of the solutions for such equations and investigate data dependence of their solutions.

The most robust treatment of the inverse acoustic scattering problem is based on the reversion of the Born-Neumann series solution of the Lippmann-Schwinger equation. An important issue for this approach to inversion is the radius of convergence of the Born-Neumann series for Fredholm integral kernels, and especially for acoustic scattering for which the interaction depends on the square of the...

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, we propose a new numerical method for solution of urysohn two dimensional mixed volterra-fredholm integral equations of the second kind on a non-rectangular domain. the method approximates the solution by the discrete collocation method based on inverse multiquadric radialbasis functions (rbfs) constructed on a set of disordered data. the method is a meshless method, because it i...