s of PhD Theses at Irish Universities 2007 On the Asymptotic Behaviour of Deterministic and Stochastic Volterra Integro–Differential Equations

We consider the numerical solution of real time equilibrium Dyson equation, which is used in calculations dynamical properties quantum many-body systems. show that this equation can be written as a system coupled, nonlinear, convolutional Volterra integro-differential equations, for kernel depends self-consistently on solution. As typical Volterra-type computational bottleneck quadratic-scaling...

In this paper, we employed the use of Standard Integral Collocation Approximation Method to obtain numerical solutions of special higher orders linear Fredholm-Volterra Integro-Differential Equations. Power Series, Chebyshev and Legendre's Polynomials forms of approximations are used as basis functions. From the computational view points, the method is efficient, convenient, reliable and superi...

In this paper, by using the theories and methods of integral equation and computer algebra, a reliable algorithm for solving the Volterra integral equation is established, and a new Maple algorithm mainproc is established, too. Some examples are presented to illustrate the implementations of the algorithm. The results of the examples indicate that the algorithm of Taylor polynomial method is si...

In this paper, we propose a new algorithm for constructing an integral model of nonlinear dynamic system the “input–output” type in form quadratic segment Volterra integro-power series (polynomial). We consider nonparametric identification models using physically realizable piecewise linear test signals time domain. The advantage presented approach is to obtain explicit formulas calculating tra...

Nonlinear viscoelastic oscillations of a vehicle in vertical direction excited by static imbalance are considered. When taking into account the rheological properties suspension material and spring, Boltzmann-Volterra principle was used. Mathematical models problem under consideration obtained, which described systems nonlinear integro-differential equations. A solution method based on quadratu...

In this paper, we present some results on the existence of periodic solutions to Volterra integro-differential equations of neutral type. The main idea is to show the convergence of an equibounded sequence of periodic solutions of certain limiting equations which are of finite delay. This makes it possible to apply the existing Liapunov-Razumikhin technique for neutral equations with finite del...

This paper is concerned with obtaining the approximate solution of Fredholm-Volterra integro-differential equations. Properties of the Shannon wavelets and connection coefficients are first presented. We design a numerical scheme for these equations using the Galerkin method incorporated with the Shannon wavelets approximation and the connection coefficients. We will show that using this techni...

A numerical method based on Legendre multi-wavelets is applied for solving Lane-Emden equations which form Volterra integro-differential equations. The Lane-Emden equations are converted to Volterra integro-differential equations and then are solved by the Legendre multi-wavelet method. The properties of Legendre multi-wavelets are first presented. The properties of Legendre multi-wavelets are ...