Sinc-collocation scheme is one of the new techniques used in solving numerical problems involving integral equations. This method has been shown to be a powerful numerical tool for finding fast and accurate solutions. So, in this paper, some properties of the Sinc-collocation method required for our subsequent development are given and are utilized to reduce integral equation of the first kind ...

In this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm Ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. We applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. The main properties of deterministic difference schemes,...

One of the main problems in computer graphics is to solve the global illumination problem, which is given by a Fredholm integral equation of the second kind, called the radiance equation (REQ). In order to achieve realistic images, a very complex kernel of the integral equation, modelling all physical effects of light, must be considered. Due to this complexity Monte Carlo methods seem to be an...

We derive bridges from general multidimensional linear non time-homogeneous processes using only the transition densities of the original process giving their integral representations (in terms of a standard Wiener process) and so-called anticipative representations. We derive a stochastic differential equation satisfied by the integral representation and we prove a usual conditioning property ...

The Fredholm integral equation of the second kind is of widespread use in many realms of engineering and applied mathematics. Among the variety of numerical solutions to this equation, the qudrature method and its modification are remarkable. The latter aims at reducing the computational complexity of the quadrature method. In this paper, we present Mathematica programs that utilize the modifie...

A numerical method for solving nonlinear Fredholm-Volterra integral equations of general type is presented. This method is based on replacement of unknown function by truncated series of well known Chebyshev expansion of functions. The quadrature formulas which we use to calculate integral terms have been imated by Fast Fourier Transform (FFT). This is a grate advantage of this method which has...

The two-point time and temperature dependent correlation functions for the XX0 one-dimensional model in constant magnetic field are represented (in the thermodynamical limit) as Fredholm determinants of linear integral operators.

A superprocess with dependent spatial motion and interactive immigration is constructed as the pathwise unique solution of a stochastic integral equation carried by a stochastic flow and driven by Poisson processes of one-dimensional excursions. Mathematics Subject Classification (2000): Primary 60J80; Secondary 60G57, 60H20

In a 1977 paper of McCoy, Tracy and Wu [2] there appeared for the first time the solution of a Painlevé equation in terms of Fredholm determinants of integral operators. Specifically, it was shown that a one-parameter family of solutions of the equation ψ ′′ (t) + t −1 ψ ′ (t) = 1 2 sinh 2ψ + 2α t −1 sinh ψ, (1) a special case of the Painlevé III equation, is given by ψ(t) =