In this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear Volterra integral equations of the first and second kinds, which avoids from using starting values. An existence and uniqueness theorem is proved and convergence isverified by using an appropriate variety of the Gronwall inequality. Application of the method is demonstrated for solving the ...

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 chapter we will explain how wavelets can be used to solve integral equations. The example we use is an important integral equation in graphics, the radiosity equation. The radiosity equation governs the transport of light between surfaces under the assumption that all reflection occurs isotropically. The resulting integral equation is linear and can be analyzed as a linear operator. Sin...

In this paper, a numerical efficient method based on two-dimensional block-pulse functions (BPFs) is proposed to approximate a solution of the two-dimensional linear stochastic Volterra-Fredholm integral equation. Finally the accuracy of this method will be shown by an example.

A generalization of the linear fractional integral equation u(t) = u0 + ∂−αAu(t), 1 < α < 2, which is written as a Volterra matrix–valued equation when applied as a pixel–by–pixel technique, has been proposed for image denoising (restoration, smoothing,...). Since the fractional integral equation interpolates a linear parabolic equation and a hyperbolic equation, the solution enjoys intermediat...

Here, the solution in one, two and three dimensional for the Volterra–Fredholm integral equation of the first kind is obtained in the space L2ðXÞ C1⁄20; T , T < 1. Using a numerical method the integral equation of Volterra–Fredholm becomes a linear system of Fredholm integral equation when that the kernel of Fredholm integral takes a logarithmic form, Carleman function, generalized potential fu...

In this article, we study the existence of integral solutions for two classes of fractional order evolution equations with nondensely defined linear operators. First, we consider the nonhomogeneous fractional order evolution equation and obtain its integral solution by Laplace transform and probability density function. Subsequently, based on the form of integral solution for nonhomogeneous fra...

in this paper, we present an efficient method for determining the solution of the stochastic second kind volterra integral equations (svie) by using the taylor expansion method. this method transforms the svie to a linear stochastic ordinary differential equation which needs specified boundary conditions. for determining boundary conditions, we use the integration technique. this technique give...

In this paper we prove the existence and the uniqueness of the solutions of the Hammerstein-Volterra integral equation in the space of the absolutely continuous functions endowed with the bounded variation norm. After that, we find the resolvent of the corresponding linear integral equation in order to obtain a variation of parameters formula for the solutions of this linear equation. Finally, ...

Abstract: An integral equation method based on the Kerzman-Stein kernel for conformal mapping of smooth doubly connected regions onto an annulus A = {w : μ < |w| < 1} is presented. The theoretical development is based on the boundary integral equation for conformal mapping of doubly connected regions with Kerzman-Stein kernel derived by Razali and one of the authors [8]. However, the integral e...