in this paper, we studied the numerical solution of nonlinear weakly singular volterra-fredholm integral equations by using the product integration method. also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear volterra-fredholm integral equations. the reliability and efficiency of the proposed scheme are...

As both light transport simulation and reinforcement learning are ruled by the same Fredholm integral equation of the second kind, machine learning techniques can be used for efficient photorealistic image synthesis: Light transport paths are guided by an approximate solution to the integral equation that is learned during rendering. In analogy to recent advances in reinforcement learning for p...

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 ...

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...

in this article the nonlinear mixed volterra-fredholm integral equations are investigated by means of the modied three-dimensional block-pulse functions (m3d-bfs). this method converts the nonlinear mixed volterra-fredholm integral equations into a nonlinear system of algebraic equations. the illustrative   examples are provided to demonstrate the applicability and simplicity of our   scheme.

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...

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) =

Fuzzy integral equations play major roles in various areas, therefore a new method for finding a solution of the Fredholm fuzzy integral equation is presented. This method converts the fuzzy integral equation into linear system by using the Taylor series. For this scope, first the Taylor expansion of unknown function is substituted in parametric form of the given equation. Then we differentiate...

Finite-dimensional perturbing operators are constructed using some incomplete information about eigen-solutions of an original and/or adjoint generalized Fredholm operator equation (with zero index). Adding such perturbing operator to the original one reduces the eigen-space dimension and can, particularly, lead to an unconditionally and uniquely solvable perturbed equation. For the second kind...