In this paper we study the existence of classical solutions for a class of abstract neutral integro-differential equation with unbounded delay. A concrete application to partial neutral integro-differential equations is considered.

will be employed in the analysis of the principle properties of the collocation approximations; the extension to nonlinear equations is straightforward (cf. [1, p. 225]). High-order numerical methods for VIDEs with weakly singular kernels may be found in [1,2,6,7,8]. In this note we shall consider collocation methods for VIDE (1.1), based on Brunner's approach [1]. The following method and nota...

We have elaborated the numerical schemes of reduction method by FaberLaurent polynomials for the approximate solution of system of singular integrodifferential equations. The equations are defined on the arbitrary smooth closed contour. The theoretical foundation has been obtained in Lebesgue spaces. Key–Words: singular integrodifferential equations, reduction method, Lebesgue spaces

In this paper we consider a risk model with two classes of insurance risks in the presence of a multi-layer dividend startegy. We assume that the two claim counting processes are, respectively, Poisson and Sparre Andersen with generalized Erlang(2) claim inter-arrival times. We derive an integro-differential equation system for the Gerber-Shiu functions for surplus-dependent premium rates and a...

Spline curves are very prominent in the mathematics due to their simple construction, accuracy of assessment and ability approximate complicated structures into interactive curved designs. A spline is a smooth piece-wise polynomial function. The primary goal this study use extended cubic B-spline (ExCuBS) functions with new second order derivative approximation obtain numerical solution weakly ...

The effect of non-stationary external forces on the vibration pipelines made composite materials is investigated in paper. A mathematical model pipeline developed, considering viscosity properties structure and base material, axial forces, internal pressure, resistance disturbances. viscoelastic conveying fluid under vibrations constructed based Boltzmann-Volterra integral model. to study a Eul...