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Turkish Journal of Mathematics

DOI

10.3906/mat-1508-50

Abstract

In this paper, we present a numerical method to approximate the solution of linear stochastic Ito-Volterra integral equations driven by fractional Brownian motion with Hurst parameter $ H \in (0,1)$ based on a stochastic operational matrix of integration for generalized hat basis functions. We obtain a linear system of algebraic equations with a lower triangular coefficients matrix from the linear stochastic integral equation, and by solving it we get an approximation solution with accuracy of order $ \emph{O}(h^2)$. This numerical method shows that results are more accurate than the block pulse functions method where the rate of convergence is $ \emph{O}(h)$. Finally, we investigate error analysis and with some examples indicate the efficiency of the method.

First Page

611

Last Page

624

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Mathematics Commons

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