CAS Wavelets Stochastic Operational Matrix of Integration and its Application for Solving Stochastic Itô-Volterra Integral Equations

Abstract

This article provides an effective technique for solving stochastic Itˆo-Volterra integral equations using Cosine and Sine (CAS) wavelets. A novel stochastic operational matrix of integration of CAS wavelets is developed in this article for solving stochastic Itˆo-Volterra integral equations. Stochastic Itˆo-Volterra integral equation can be reduced to a system of algebraic equations using the newly generated stochastic operational matrix of integration of CAS wavelets along with the operational matrix of integration of CAS wavelets. These system of algebraic equations can be solved using appropriate methods. Convergence and the error analysis of the proposed technique is studied in detail. Numerical examples are presented in order to show the efficiency and reliability of the proposed method.

Key words and phrases. CAS wavelets, Brownian motion, stochastic Itˆo-Volterra integral equations.

2000 Mathematics Subject Classification. 65T60, 60H20, 65C30