A method is used to solve the Fredholm–Volterra integral equation of the first kind in the space L2ðXÞ Cð0; T Þ, X 1⁄4 ðx; yÞ 2 X: ffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 þ y2 p n 6 a; z 1⁄4 0 o and T < 1: The kernel of the Fredholm integral term considered in the generalized potential form belongs to the class Cð1⁄2X 1⁄2X Þ, while the kernel of the Volterra integral term is a positive an...

In this paper we intend to offer new numerical methods to solvethe fuzzy Fredholm- Volterra integral equations of the firstkind $(FVFIE-1)$. Some examples are investigated to verify convergence results and to illustrate the efficiently of the methods.  

It has been shown that a normal S-iterative method converges to the solution of a mixed type Volterra-Fredholm functional nonlinear integral equation. Furthermore, a data dependence result for the solution of this integral equation has been proven.

We consider a nonlinear Volterra-Fredholm integral equation NVFIE of the second kind. The Volterra kernel is time dependent, and the Fredholm kernel is position dependent. Existence and uniqueness of the solution to this equation, under certain conditions, are discussed. The block-byblock method is introduced to solve such equations numerically. Some numerical examples are given to illustrate o...

the main purpose of this article is to increase the efficiency of the least squares method in numerical solution of ill-posed functional and physical equations. determining the least squares of a given function in an arbitrary set is often an ill-posed problem. in this article, by defining artificial constraint and using lagrange multipliers method, the attempt is to turn -dimensional least squ...

We propose a new method, called the textit{the weighted space method}, for the study of the generalized Hyers-Ulam-Rassias stability. We use this method for a nonlinear functional equation, for Volterra and Fredholm integral operators.

Abstract: In this paper, a numerical method to solve nonlinear Fredholm integral equations of second kind is proposed and some numerical notes about this method are addressed. The method utilizes Chebyshev wavelets constructed on the unit interval as a basis in the Galerkin method. This approach reduces this type of integral equation to solve a nonlinear system of algebraic equation. The method...

We consider a Fredholm integral equation of the second kind in L1([a, b],C), with a weakly singular kernel. Sufficient conditions are given for the existence and uniqueness of the solution. We adapt the product integration method proposed in C0([a, b],C) to apply it in L1([a, b],C), and discretize the equation. To improve the accuracy of the approximate solution, we use different iterative refi...

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&apos;s functions, the mixed boundary value problem is written as a dual integral equation. employing further mathematica...