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

Authors:
M. Khodabin;K. Maleknejad;M. Rostami;M. Nouri
Affiliations:
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran;Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran;Department of Mathematics, Naragh Branch, Islamic Azad University, Naragh, Iran;Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
Venue:
Computers & Mathematics with Applications
Year:
2012

Citing 5
Cited 0

Stochastic differential equations (3rd ed.): an introduction with applications

Stochastic differential equations (3rd ed.): an introduction with applications
Block Pulse Functions and Their Applications in Control Systems

Block Pulse Functions and Their Applications in Control Systems
Numerical solution of an integral equations system of the first kind by using an operational matrix with block pulse functions

International Journal of Systems Science
Numerical solution of random differential equations: A mean square approach

Mathematical and Computer Modelling: An International Journal
Numerical solution of stochastic differential equations by second order Runge-Kutta methods

Mathematical and Computer Modelling: An International Journal

Quantified Score

Hi-index	0.09

Visualization

Abstract

In this paper, we obtain stochastic operational matrix of block pulse functions on interval [0,1) to solve stochastic Volterra-Fredholm integral equations. By using block pulse functions and their stochastic operational matrix of integration, the stochastic Volterra-Fredholm integral equation can be reduced to a linear lower triangular system which can be directly solved by forward substitution. We prove that the rate of convergence is O(h). Furthermore, the results show that the approximate solutions have a good degree of accuracy.