In this paper, we propose and analyze an efficient matrix method based on Bell polynomials for numerically solving nonlinear Fredholm- Volterra integral equations. For this aim, first we calculate operational matrix of integration and product based on Bell polynomials. By using these matrices, nonlinear Fredholm-Volterra integral equations reduce to the system of nonlinear algebraic equations w...

This paper is concerned with systems of functional differential equations with either finite or infinite delay. We give conditions on the system and on a Liapunov function to ensure that the zero solution is asymptotically stable. Section 2 is devoted to finite delay, Section 3 to infinite delay, and Section 4 to examples. The remainder of this section introduces the problem for the finite dela...

In this study, a new application of Taylor expansion is considered to estimate the solution of Volterra-Fredholm integral equations (VFIEs) and systems of Volterra-Fredholm integral equations (SVFIEs). Our proposed method is based upon utilizing the nth-order Taylor polynomial of unknown function at an arbitrary point and employing integration method to convert VFIEs into a system of linear equ...

We propose an efficient mesh-less method for functional integral equations. Its convergence analysis has been provided. It is tested via a few numerical experiments which show the efficiency and applicability of the proposed method. Attractive numerical results have been obtained.