This paper applies He’s variational iteration method for solving two systems of Volterra integro-differential equations. The solution process is illustrated and various physically relevant results are obtained. Comparison of the obtained results with exact solutions shows that the used method is an effective and highly promising method for various classes of both linear and nonlinear integro-di...

in this paper, we apply the differential transform (dt) method for finding approximate solution of the system of linear and nonlinear volterra integro-differential equations with variable coefficients, especially of higher order. we also obtain an error bound for the approximate solution. since, in this method the coefficients of taylor series expansion of solution is obtained by a recurrence r...

NEW ALGORITHMS FOR NUMERICAL SOLUTION OF NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS OF THIRD ORDER USING HAAR WAVELETS M. Fayyaz a and M. Azram b * Department of Computer Science, CECOS University Peshawar, Pakistan. [email protected] b Faculty of Engineering, IIUM, Kuala Lumpur 50728, Malaysia. [email protected] ABSTRACT: This paper deals with the extension of earlier work [3] (designed for Fre...

in this paper, first the properties of one and two-dimensional differential transforms are presented.next, by using the idea of differential transform, we will present a method to find an approximate solution fora volterra integro-partial differential equations. this method can be easily applied to many linear andnonlinear problems and is capable of reducing computational works. in some particu...

An efficient hybrid method is developed to approximate the solution of the high-order nonlinear Volterra-Fredholm integro-differential equations. The properties of hybrid functions consisting of block-pulse functions and Lagrange interpolating polynomials are first presented. These properties are then used to reduce the solution of the nonlinear Volterra-Fredholm integro-differential equations ...

In this paper, we apply the differential transform (DT) method for finding approximate solution of the system of linear and nonlinear Volterra integro-differential equations with variable coefficients, especially of higher order. We also obtain an error bound for the approximate solution. Since, in this method the coefficients of Taylor series expansion of solution is obtained by a recurrence r...

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...

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...