A method is used to solve the Fredholm-Volterra integral equation of the first kind in the space L2(Ω)×C(0,T ),Ω = {(x,y) : √ x2+y2 ≤ a}, z = 0, and T <∞. The kernel of the Fredholm integral term considered in the generalized potential form belongs to the class C([Ω]×[Ω]), while the kernel of Volterra integral term is a positive and continuous function that belongs to the class C[0,T ]. Also in...

In this paper, a reliable iterative approach, for solving a wide range of linear and nonlinear Volterra-Fredholm integral equations is established. First the approach considers a discretized form of the integral terms where considering some conditions on the kernel of the integral equation it is proved that solution of the discretized form converges to the exact solution of the problem. Then th...

In this paper a numerical technique is presented for the solution of fuzzy linear Volterra-Fredholm-Hammerstein integral equations. This method is a combination of collocation method and radial basis functions(RBFs).We first solve the actual set are equivalent to the fuzzy set, then answer 1-cut into the equation. Also high convergence rates and good accuracy are obtain with the propose method ...

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...

In this work, we introduce a novel method for solving two-dimensional fuzzy Fredholm integral equations of the second kind (2D-FFIE-2). We use new representation of parametric form of fuzzy numbers and convert a two-dimensional fuzzy Fredholm integral equation to system of two-dimensional Fredholm integral equations of the second kind in crisp case. We can use Adomian decomposition method for n...

In 1982, Dubois and Prade [4, 5] first introduced the concept of integration of fuzzy functions. Kaleva [7] studied the measurability and integrability for the fuzzy set-valued mappings of a real variable whose values are normal, convex, upper semicontinuous, and compactly supported by fuzzy sets in Rn. Existence of solutions of fuzzy integral equations has been studied by several authors [1, 2...

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.

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, a nonlinear volterra-fredholm integral equation of the first kind is solved by using the homotopy analysis method (ham). in this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by ham. the approximate solution of this equation is calculated in the form of a series which its components are computed easily. the accuracy...