Asymptotic Representation of the Solutions of Linear Volterra Difference Equations

A finite difference method for the smooth solution of linear Volterra integral equations

The present paper proposes a fast numerical method for the linear Volterra integral equations withregular and weakly singular kernels having smooth solutions. This method is based on the approx-imation of the kernel, to simplify the integral operator and then discretization of the simpliedoperator using a forward dierence formula. To analyze and verify the accuracy of the method, weexamine samp...

On the Asymptotic Stability of Linear Volterra Difference Equations of Convolution Type

We show that the condition |a|+ ∣∣∣∑+∞ l=0 bl∣∣∣ < 1 is not necessary, though sufficient, for the asymptotic stability of xn+1 = axn + ∑+∞ l=0 bn−lxl. We prove the existence of a class of Volterra difference equations that violate this condition but whose zero solutions are asymptotically stable.

Numerical Solutions of Special Class of Systems of Non-Linear Volterra Integro-Differential Equations by a Simple High Accuracy Method

Asymptotic properties of solutions of difference equations with several delays and Volterra summation equations

We study a scalar linear difference equation with several delays by transforming it to a system of Volterra equations without delays. The results obtained for this system are then used to establish oscillation criteria and asymptotic properties of solutions of the considered equation.

A computational wavelet method for numerical solution of stochastic Volterra-Fredholm integral equations

A Legendre wavelet method is presented for numerical solutions of stochastic Volterra-Fredholm integral equations. The main characteristic of the proposed method is that it reduces stochastic Volterra-Fredholm integral equations into a linear system of equations. Convergence and error analysis of the Legendre wavelets basis are investigated. The efficiency and accuracy of the proposed method wa...