In this paper, two collocation methods based on the shifted Legendre polynomials are proposed for solving system of nonlinear Fredholm-Volterra integro-differential equations. The equation considered in paper involves derivative unknown functions integral term, which makes its numerical solution more complicated. We first introduce a single-step method interval [0, 1]. Next, multi-step version ...

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...

Fractional calculus, which deals with the concept of fractional derivatives and integrals, has become an important area research, due to its ability capture memory effects non-local behavior in modeling real-world phenomena. In this work, we study a new class Volterra–Fredholm integro-differential equations, involving Caputo–Katugampola derivative. By applying Krasnoselskii Banach fixed-point t...

In this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. We approximate the exact solution by use of Radial Basis Function(RBF) collocation method. This techniqueplays an important role to reduce a fractional dierential equation to a system of equations. The numerical results demonstrate the accuracy and ability of this me...