In this paper, a numerical matrix method is used to solve the systems of high-order linear Fredholm integro-differential equations with variable coefficients under mixed conditions. The technique consists collocation points and Morgan-Voyce polynomials. residual error functions solutions are also presented. Firstly, approximate formed secondly, an problem constituted in favor function. computed...

Abstract In this study, linear Fredholm fractional integro-differential equations (FIDEs) are numerically solved, where the derivative is considered in Caputo sense. work, least squares method (LSM) using a compact combination of shifted Chebyshev polynomials (SCP) first Kind applied to solving class FIDEs. Our aim write unknown function as series SCP, and then reduce problem system algebraic e...

in this study, a new and ecient approach is presented for numerical solution offredholm integro-dierential equations (fides) of the second kind on unbounded domainwith degenerate kernel based on operational matrices with respect to generalized laguerrepolynomials(glps). properties of these polynomials and operational matrices of integration,dierentiation are introduced and are ultilized to r...

A class of singular integro-differential equations in Lebesgue spaces are studied. There are many applications of the singular integro-differential equations discussed in this paper. An example in modeling the stress distribution of an elastic medium with holes is discussed in the paper. Direct numerical schemes using a collocation method and a mechanical quadrature rule designed for the singul...

This paper presents a ε-uniform and reliable numerical scheme to solve second-order singularly perturbed Volterra–Fredholm integro-differential equations. Some properties of the analytical solution are given, finite difference is established on non-uniform mesh by using interpolating quadrature rules linear basis functions. An error analysis successfully carried out Boglaev–Bakhvalov-type mesh....

in this paper, a novel hybrid method based on learning algorithmof fuzzy neural network and newton-cotesmethods with positive coefficient for the solution of linear fredholm integro-differential equation of the second kindwith fuzzy initial value is presented. here neural network isconsidered as a part of large field called neural computing orsoft computing. we propose alearning algorithm from ...