Stability of Nonlinear Stochastic Volterra Difference Equations with Respect to a Fading Perturbation

Fuzzy difference equations of Volterra type

In this work we introduce the notion of fuzzy volterra dierence equations and study the dynamicalproperties of some classes of this type of equations. We prove some comparison theorems for theseequations in terms of ordinary volterra dierence equations. Using these results the stability of thefuzzy nonlinear volterra dierence equations is investigated.

Numerical solutions of two-dimensional linear and nonlinear Volterra integral equations: Homotopy perturbation method and differential transform method

Wilson wavelets for solving nonlinear stochastic integral equations

A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It^{o}-Volterra integral equations. To do this a new stochastic operational matrix of It^{o} integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operat...

General Method of Lyapunov Functionals Construction in Stability Investigations of Nonlinear Stochastic Difference Equations with Continuous Time

The general method of Lyapunov functionals construction has been developed during the last decade for stability investigations of stochastic differential equations with aftereffect and stochastic difference equations. After some modification of the basic Lyapunov type theorem this method was successfully used also for difference Volterra equations with continuous time. The latter often appear a...

Convergence of Legendre wavelet collocation method for solving nonlinear Stratonovich Volterra integral equations

In this paper, we apply Legendre wavelet collocation method to obtain the approximate solution of nonlinear Stratonovich Volterra integral equations. The main advantage of this method is that Legendre wavelet has orthogonality property and therefore coefficients of expansion are easily calculated. By using this method, the solution of nonlinear Stratonovich Volterra integral equation reduces to...