TWO-STEP ORDER 3/2 STRONG METHOD FOR APPROXIMATING STOCHASTIC DIFFERENTIAL EQUATIONS

Yazid Alhojilan

Yazid Alhojilan Department of Mathematics, College of Science, Qassim University, Saudi Arabia

Article ID: 2398

Keywords: stochastic differential equations; pathwise approximation; Runge-Kutta method; Itô-Taylor expansion

Abstract

In this paper, we consider two-step order strong scheme for getting numerical solutions of stochastic differential equations (SDEs) of order 3/2. It follows a new technique based on replacing stochastic integrals $I_\alpha$ by random variables. Thus we do not need to calculate $I_\alpha$. We employ Itô-Taylor expansion and Runge-Kutta method to get the approximate solutions of the desired order. The experimental results of the approximation method and its error are provided to confirm the validity of the method.

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