Beginning from the creator of integro-differential equations Volterra, many scientists have investigated these equations. Classic method for solving integro-differential equations is the quadratures method that is successfully applied up today. Unlike these methods, Makroglou applied hybrid methods that are modified and generalized in this paper and applied to the numerical solution of Volterra...

In the research, nonlinear volterra partial integro-differential equation is considered. This paper compares the Homotopy Perturbation Method (HPM) with Variational Iteration Method (VIM) for solving this equation. Compared with the Adomian Decomposition Method (ADM), the methods used for this equation need less work. The results of applying these methods show the simplicity and efficiency of t...

The present paper deals with the numerical solution for a general form of system nonlinear Volterra delay integro-differential equations (VDIDEs). main purpose this work is to provide a...

The spatial discretization of initial-boundary-value problems for (nonlinear) parabolic or hyperbolic PDEs with memory terms leads to (large) systems of Volterra integro-differential equations (VIDEs). In this paper we study the efficient numerical solution of such systems by methods based on linear multistep formulas, using special factorization (or splitting) techniques in the iterative solut...

In this paper, the new iterative method with a reliable algorithm is applied to the systems of Volterra integro-differential equations. The method is useful for both linear and nonlinear equations. By using this method, the solutions are obtained in series form. Two linear and one nonlinear system of the equations are given to verify the reliability and efficiency of the method. Beside this, th...

We investigate an h-p version of the continuous Petrov-Galerkin method for the nonlinear Volterra functional integro-differential equations with vanishing delays. We derive h-p version a priori error estimates in the L-, Hand L-norms, which are completely explicit in the local discretization and regularity parameters. Numerical computations supporting the theoretical results are also presented.

This paper deals with the stability of Runge–Kutta methods for a class of stiff systems of nonlinear Volterra delay-integro-differential equations. Two classes of methods are considered: Runge–Kutta methods extended with a compound quadrature rule, and Runge– Kutta methods extended with a Pouzet type quadrature technique. Global and asymptotic stability criteria for both types of methods are de...

In recent years, some promising approximate analytical solutions are proposed, such as exp-function method [1], homotopy perturbation method [2 – 11], and variational iteration method (VIM) [12 – 17]. The variational iteration method is the most effective and convenient one for both weakly and strongly nonlinear equations. This method has been shown to effectively, easily, and accurately solve ...

In this paper, we prove the existence and uniqueness of a nonlinear perturbed stochastic fractional integro-differential equation of Volterra-Itô type involving nonlocal initial condition by using the theory of admissibility of integral operator and Banach fixed-point principle. Also the stability and boundedness of the second moments of the stochastic solution are studied. In addition, an appl...

The homotopy analysis method [1, 2], is developed to search the accurate asymptotic solutions of nonlinear problems. This technique has been successfully applied to many nonlinear problems such as the viscous flows of non-Newtonian fluids [3, 4], the Korteweg-de Vries-type equations [5, 6], nonlinear heat transfer [7, 8], finance problems [9, 10], Riemann problems related to nonlinear shallow w...