In this paper, we apply the Variational iteration method and homotopy perturbation method for solving linear and nonlinear partial integro-differential equation (PIDE). The efficiency and accuracy of the methods is validated by its application to several distinct test problems which have exact solutions. The results of applying these methods show the simplicity and efficiency of these methods.

We show that fully nonlinear elliptic PDEs (which may not have classical solutions) can be approximated with integro-differential equations which have C solutions. For these approximated equation we prove a uniform C estimate. We also study the rate of convergence.

in this article we have considered a non-standard finite difference method for the solution of second order  fredholm integro differential equation type initial value problems. the non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the fredholm integro-differential equation into a system of equations. we have also developed a numerical met...

In this paper, we are focused upon the global uniqueness results for a stochastic integro-differential equation in Fréchet spaces. The main results are proved by using the resolvent operators combined with a nonlinear alternative of Leray-Schauder type in Fréchet spaces due to Frigon and Granas. As an application, a controllability result with one parameter is given to illustrate the theory.

This paper is concerned with the existence of almost periodic and pseudo almost solutions for a nonlinear integro-differential equation with neutral delay, which arise in epidemic problems. By using almost periodic functions theory and fixed point theory, we obtain the results. Two examples are given to illustrate our results. In addition, an application to nonautonomous differential equations ...

A quasi-static mixed boundary value problem of incremental elasto-plasticity for a continuously inhomogeneous body is considered. Using the two-operator Green-Betti formula and the fundamental solution of a reference homogeneous linear elasticity problem, with frozen initial or tangent elastic coefficients, a boundary-domain integro-differential formulation of the elasto-plastic problem is pres...

In this article, we apply the operational matrix to find the numerical solution of two- dimensional nonlinear Volterra integro-differential equation (2DNVIDE). Form this prospect, two-dimensional shifted Legendre functions (2DSLFs) has been presented for integration, product as well as differentiation. This method converts 2DNVIDE to an algebraic system of equations, so the numerical solution o...

We consider a nonlinear Volterra integro-differential equation with periodic solution, a special case of which has been used in modeling hematopoiesis dynamics. Some analytical results concerning existence and uniqueness of a positive periodic solution are presented together with some numerical results based on the reformulation of the equation as a system of ODEs and also from its direct solut...

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. Finally, by ...

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 ...