In the research, special type of linear volterra integro-differential equations is considered. This paper compares the Homotopy perturbation method (HPM) with finite difference method for solving these equations. HPM is an analytical procedure for finding the solutions of problems which is based on the constructing a Homotopy with an imbedding parameter p that is considered as a small parameter...

the purpose of this study is to present an approximate numerical method for solving high order linear fredholm-volterra integro-differential equations in terms of rational chebyshev functions under the mixed conditions. the method is based on the approximation by the truncated rational chebyshev series. finally, the effectiveness of the method is illustrated in several numerical examples. the p...

A numerical method based on Legendre multi-wavelets is applied for solving Lane-Emden equations which form Volterra integro-differential equations. The Lane-Emden equations are converted to Volterra integro-differential equations and then are solved by the Legendre multi-wavelet method. The properties of Legendre multi-wavelets are first presented. The properties of Legendre multi-wavelets are ...

here a posteriori error estimate for the numerical solution of nonlinear voltena- hammerstein equations is given. we present an error upper bound for nonlinear voltena-hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of brunner for these problems (the implicitly linear collocation method).we al...

In this paper, we present some results on the existence of periodic solutions to Volterra integro-differential equations of neutral type. The main idea is to show the convergence of an equibounded sequence of periodic solutions of certain limiting equations which are of finite delay. This makes it possible to apply the existing Liapunov-Razumikhin technique for neutral equations with finite del...

This paper describes an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type. This method can be extended to functional differential and integro-differential equations. For showing efficiency of the method we give some numerical examples.

‎‎‎‎‎‎‎‎‎‎‎‎‎This paper aims to construct a general formulation for the shifted Jacobi operational matrices of integration and product‎. ‎The main aim is to generalize the Jacobi integral and product operational matrices to the solving system of Fredholm and Volterra integro--differential equations‎ which appear in various fields of science such as physics and engineering. ‎The Operational matr...

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...

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 ...