SIMULATION OF TWO-STEP ORDER 2 IMPLICIT STRONG METHOD FOR APPROXIMATING STRATONOVICH STOCHASTIC DIFFERENTIAL EQUATIONS

Yazid Alhojilan

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

Article ID: 2421

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

Abstract

This paper introduces a novel two-step order strong scheme to numerically solve Stratonovich Stochastic Differential Equations (SDEs) of order 2. The approach involves a unique technique that replaces stochastic integrals $J_\alpha$ with random variables, eliminating the need for their explicit calculation. The methodology combines the Stratonovich-Taylor expansion with the Runge-Kutta method to obtain approximate solutions with the desired order of accuracy. To validate the method’s effectiveness, the paper includes experimental results that assess the approximation quality and quantify the associated errors.

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