this paper presents a computational method for solving two types of integro-differential equations, system of nonlinear high order volterra-fredholm integro-differential equation(vfides) and nonlinear fractional order integro-differential equations. our tools for this aims is operational matrices of integration and fractional integration. by this method the given problems reduce to solve a syst...

in this letter, the numerical scheme of nonlinear volterra-fredholm integro-differential equations is proposed in a reproducing kernel hilbert space (rkhs). the method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. the nonlinear terms are replaced by its taylor series. in this technique, the nonlinear volterra-fredholm integr...

In this note, convex Homotopy perturbation method (HPM) is presented for the approximate solution of the linear Fredholm-Volterra integral and integro-differential equation. Convergence and rate of convergence of the HPM are proved for both equations. Five numerical examples are provided to verify the validity and accuracy of the proposed method. Example reveals that HPM is very accurate and si...

In this paper we discuss the collocation method for a large class of Fredholm linear integro-differential equations. It will be shown that, when a certain higher order interpolation operation is added to the collocation solution of this equation, the new approximations will, under suitable assumptions, admit a multiterm error expansion in even powers of the step-size h. Based on this expansion,...

We compare piecewise linear and polynomial collocation approaches for the numerical solution of a Fredholm integro-differential equations modelling neural networks. Both approaches combine the use of Gaussian quadrature rules on an infinite interval of integration with interpolation to a uniformly distributed grid on a bounded interval. These methods are illustrated by numerical experiments on ...

in this paper, an effective direct method to determine the numerical solution of linear and nonlinear fredholm and volterra integral and integro-differential equations is proposed. the method is based on expanding the required approximate solution as the elements of chebyshev cardinal functions. the operational matrices for the integration and product of the chebyshev cardinal functions are des...

In this manuscript, we analyze the solution for class of linear and nonlinear Caputo fractional Volterra Fredholm integro-differential equations with time varying delay. Also, demonstrate stability analysis these equations. Our paper provides a convergence semi-analytical approximate method It would be desirable to point out results.

In this study, the numerical solution of Fredholm integro–differential equation is discussed in a reproducing kernel Hilbert space. A reproducing kernel Hilbert space is constructed, in which the initial condition of the problem is satisfied. The exact solution u x ð Þ is represented in the form of series in the space W 2 2 ½a; bŠ. In the mean time, the n-term approxima te solution u n ðxÞ is o...