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_α 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.

stochastic differential equations, pathwise approximation, Runge-Kutta method, Stratonovich-Taylor expansion.

Received: October 4, 2023;  Accepted: November 24, 2023; Published: November 30, 2023

How to cite this article: Yazid Alhojilan, Simulation of two-step order 2 implicit strong method for approximating Stratonovich stochastic differential equations, Advances in Differential Equations and Control Processes 30(4) (2023), 385-394. http://dx.doi.org/10.17654/0974324323021

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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