Integro-differential equations arise in modeling various physical and engineering problems. Several numerical and analytical methods have been developed to solving such equations. We introduce the OHAM (Optimal Homotopy Asymptotic Method) for solving nonlinear integro-differential equations. Several examples for solving integro-differential equations are presented to illustrate the reliability ...

the main purpose of this paper is to consider adomian's decomposition method in non-linear volterra integro-differential equations. the advantages of this method, compared with the recent numerical techniques (in particular the implicitly linear collocation methods) , and the convergence of adomian's method applied to such nonlinear integro-differential equations are discussed. finall...

This study introduced new technique which is based on a combination of the least-squares (LST) with Chebyshev and Legendre polynomials for finding approximate solutions higher-order linear Fredholm-Volterra integro-differential equations (FVIDEs) subject to mixed conditions. Two examples second third-order FVIDEs are considered illustrate proposed method, numerical results comprised demonstrate...

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 useful matrix approach for high-order linear Fredholm integro-differential equations with initial boundary conditions expressed as Lucas polynomials is proposed. Using equationwhich equivalent to set of algebraic the method transforms equation. When compared other methods that have been proposed in literature, numerical results from suggested technique reveal it effective and p...

Recent developments have shown that the widely used simplified differential model of Eringen’s nonlocal elasticity in nanobeam analysis is not equivalent to corresponding and initially proposed integral models, pure two-phase model, all cases loading boundary conditions. This has resolved a paradox with solutions are line expected softening effect theory appears other cases. In addition, it rev...

High order integro-differential equations (IDE), especially nonlinear, are usually difficult to solve even for approximate solutions. In this paper, we give a high accurate compact finite difference method to efficiently solve integro-differential equations, including high order and nonlinear problems. By numerical experiments, we show that compact finite difference method of integro-differenti...

 Abstract: There are some methods for solving integro-differential equations. In this work, we solve the general-order Feredholm integro-differential equations. The Petrov-Galerkin method by considering Chebyshev multiwavelet basis is used. By using the orthonormality property of basis elements in discretizing the equation, we can reduce an equation to a linear system with small dimension. For ...

In this paper, we propose a different way for solving systems of nonlinear Fredholm integral equations the second kind. We construct our new strategy in two steps, through beginning with linearization phase system by applying Newton method, then pass to discretization some involved operator using Nystr\"{o}m method. The convergence analysis method is proved under necessary conditions. At last, ...