Numerical Solution of Stochastic Volterra-Fredholm Integral Equations Using Improvement of Block Pulse Functions
Ayyubi Ahmad

Topografi Kodam XVIII/Kasuari, Manokwari Selatan, Indonesia

Abstract

A numerical method based on the improvement of block pulse functions (IBPFs) is used to solve the stochastic Volterra-Fredholm integral equations. We obtain a stochastic integration operational matrix for an improvement of block pulse functions on the interval [0,1). By using the improvement of block pulse functions and its stochastic integration operational matrix, the problem in this research can be simplified into a system of linear algebraic equations which is used to obtain an approximate solution of the stochastic Volterra-Fredholm integral equations. Therefore, the convergence and error analyzes of the methods used were investigated. Several examples are given to demonstrate the efficiency and accuracy of the method.

Keywords: Brownian Motion, Improvement of Block Pulse Functions, Ito Integral, Stochastic Integration Operational Matrix, Stochastic Volterra-Fredholm Integral Equations.

Topic: Probability and Stochastic Analysis