Numerical approach for solving stochastic Volterra–Fredholm integral equations by stochastic operational matrix

A numerical method for solving m-dimensional stochastic Itô-Volterra integral equations by stochastic operational matrix

Numerical approach for solving nonlinear stochastic Ito-Volterra integral equations using Fibonacci operational matrices

A Numerical Method for Solving Stochastic Volterra-Fredholm Integral Equation

In this paper, we propose a numerical method based on the generalized hat functions (GHFs) and improved hat functions (IHFs) to find numerical solutions for stochastic Volterra-Fredholm integral equation. To do so, all known and unknown functions are expanded in terms of basic functions and replaced in the original equation. The operational matrices of both basic functions are calculated and em...

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...

Numerical implementation a stochastic operational matrix for solving a nonlinear backward stochastic differential equation

In this paper, a computational technique is proposed for solving a nonlinear backward stochastic differential equation involving standard Brownian motion. The method is presented via the block pulse functions in combination with the collocation method. With using this approach, the nonlinear backward stochastic differential is reduced to a stochastic nonlinear system of 2m equations and 2m unkn...