Mean Square Summability of Solution of Stochastic Difference Second-Kind Volterra Equation with Small Nonlinearity

Research Article Mean Square Summability of Solution of Stochastic Difference Second-Kind Volterra Equation with Small Nonlinearity

Difference equations with continuous time are popular enough with researches [1–8]. Volterra equations are undoubtedly also very important for both theory and applications [3, 8–12]. Sufficient conditions for mean square summability of solutions of linear stochastic difference second-kind Volterra equations were obtained by authors in [10] (for difference equations with discrete time) and [8] (...

NUMERICAL SOLUTION OF LINEAR FREDHOLM AND VOLTERRA INTEGRAL EQUATION OF THE SECOND KIND BY USING LEGENDRE WAVELETS

In this paper, we use the continuous Legendre wavelets on the interval [0,1] constructed by Razzaghi M. and Yousefi S. [6] to solve the linear second kind integral equations. We use quadrature formula for the calculation of the products of any functions, which are required in the approximation for the integral equations. Then we reduced the integral equation to the solution of linear algebraic ...

Lyapunov Functionals Construction for Stochastic Difference Second-kind Volterra Equations with Continuous Time

The general method of Lyapunov functionals construction which was developed during the last decade for stability investigation of stochastic differential equations with aftereffect and stochastic difference equations is considered. It is shown that after some modification of the basic Lyapunov-type theorem, this method can be successfully used also for stochastic difference Volterra equations w...

Spline Approximation to the Solution of the Volterra Integral Equation of the Second Kind

A cubic spline approximation in C1 to the solution of a general Volterra integral equation of the second kind is constructed. Under certain conditions, convergence of the approximation and its first two derivatives is proved and error bounds are obtained. The question of stability is not examined.

Numerical Solution of Fuzzy Linear Volterra Integral Equations of the Second Kind by Homotopy Analysis Method