Affiliation:
1. Faculty of Aerospace Engineering, Polytechnic University of Bucharest, 1-7 Polizu Street, 011061 Bucharest, Romania
2. National Research and Development Institute for Gas Turbines COMOTI, 220D Iuliu Maniu, 061126 Bucharest, Romania
Abstract
Stochastic Differential Equations (SDEs) model physical phenomena dominated by stochastic processes. They represent a method for studying the dynamic evolution of a physical phenomenon, like ordinary or partial differential equations, but with an additional term called “noise” that represents a perturbing factor that cannot be attached to a classical mathematical model. In this paper, we study weak and strong convergence for six numerical schemes applied to a multiplicative noise, an additive, and a system of SDEs. The Efficient Runge–Kutta (ERK) technique, however, comes out as the top performer, displaying the best convergence features in all circumstances, including in the difficult setting of multiplicative noise. This result highlights the importance of researching cutting-edge numerical techniques built especially for stochastic systems and we consider to be of good help to the MATLAB function code for the ERK method.
Funder
University POLITEHNICA of Bucharest
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
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