Abstract This paper presents an appropriate numerical method to solve nonlinear Fredholm integro-differential equations with time delay. Its approach is based on the Taylor expansion. This method converts the integro-differential equation and the given conditions into the matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Taylor expansion coefficients, s...

In this paper‎, ‎first‎, ‎a numerical method is presented for solving a class of linear Fredholm integro-differential equation‎. ‎The operational matrix of derivative is obtained by introducing hybrid third kind Chebyshev polynomials and Block-pulse functions‎. ‎The application of the proposed operational matrix with tau method is then utilized to transform the integro-differential equations to...

‎‎‎‎‎‎‎‎‎‎‎‎‎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...

This paper presents a numerical matrix method based on Bernstein polynomials (BPs) for approximate the solution of a system of m-th order nonlinear Volterra integro-differential equations under initial conditions. The approach is based on operational matrices of BPs. Using the collocation points,this approach reduces the systems of Volterra integro-differential equations associated with the giv...

This paper proposes numerical methods for solving hybrid weakly singular integro-differential equations of the second kind. The terms in these equations are in the following order: derivative term of a state, integro-differential term of a state with a weakly singular kernel, a state, integral term of a state with a smooth kernel, and force. The original class of weakly singular integro-differe...

We consider the system of Volterra integro-dynamic equations x(t) = A(t)x(t) + ∫ t t0 B(t, s)x(s)∆s and obtain necessary and sufficient conditions for the uniform stability of the zero solution employing the resolvent equation coupled with the variation of parameters formula. The resolvent equation that we use for the study of stability will have to be developed since it is unknown for time sca...

In this paper, we give an analytical approximate solution for an integro- differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. The homotopy analysis method (HAM) is used for solving this equation. Several examples are given to reconfirm the efficiency of these algorithms. The results of applying this procedure...

 Abstract: There are some methods for solving integro-differential equations. In this work, we solve the general-order Feredholm integro-differential equations. The Petrov-Galerkin method by considering Chebyshev multiwavelet basis is used. By using the orthonormality property of basis elements in discretizing the equation, we can reduce an equation to a linear system with small dimension. For ...

In this paper, the variational iteration method proposed by Ji-Huan He is applied to solve both linear and nonlinear boundary value problems for fourth order integro-differential equations. The numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the variational iteration method is of high...