this paper has been devoted to apply the reconstruction of variational iteration method (rvim) to handle the systems of integro-differential equations. rvim has been induced with laplace transform from the variational iteration method (vim) which was developed from the inokuti method. actually, rvim overcome to shortcoming of vim method to determine the lagrange multiplier. so that, rvim method...

in this paper, we propose the chebyshev wavelet approximation for the numerical solution of a class of integro-differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields. we show that the chebyshev approximation transform an integral equation to an explicit system of linear algebraic equations. illustrative examples are included t...

In this paper we consider the Cauchy boundary value problem for the integro-differential equation utt −m ( ∫

The present study is an attempt to find a solution for Volterra's Population Model by utilizing Spectral methods based on Rational Christov functions. Volterra's model is a nonlinear integro-differential equation. First, the Volterra's Population Model is converted to a nonlinear ordinary differential equation (ODE), then researchers solve this equation (ODE). The accuracy of method is tested i...

The aim of this article is to present an efficient numerical procedure for solving mixed linear integro-differential-difference equations. Our method depends mainly on a Taylor expansion approach. This method transforms mixed linear integro-differentialdifference equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equation. The reliability a...

In this paper, a numerical method is proposed to solve FredholmVolterra fractional integro-differential equation with nonlocal boundary conditions. For this purpose, the Chebyshev wavelets of second kind are used in collocation method. It reduces the given fractional integro-differential equation (FIDE) with nonlocal boundary conditions in a linear system of equations which one can solve easily...

In this article, an adaptive least-squares mixed finite element method is studied for pseudo-parabolic integro-differential equations. The solutions of least-squares mixed weak formulation and mixed finite element are proved. A posteriori error estimator is constructed based on the least-squares functional and the posteriori errors are obtained. Keywords—Pseudo-parabolic integro-differential eq...

This paper concerns an inverse problem for an integro-differential equation related to the Basset problem. The inverse problem aims to determine a weakly singular term from the time trace at a fixed point x0 ∈ . We use the maximum principle for an integro-differential operator to derive the uniqueness of the inverse problem. Additionally, we prove the existence and uniqueness of the direct Bass...

A linear partial integro-differential equation is solved both numerically and analytically using variational iteration method. This equation typically arises in viscoelasticity and other areas. The analytic solution is represented by an infinite series.

Abstract: In this paper, motivated by the research on qualitative properties of solutions for fractional differential-integro equations, some new Gronwall-Bellman type inequalities in two independent variables are established. Based on these inequalities, explicit bounds for unknown functions concerned are derived. As for applications, we apply the inequalities established to research boundedne...