Comparison of Numerical Methods for the Kuba Oscillator

Abstract

In this study, numerical solutions of stochastic differential equation (SDE) systems have been analyzed and three different numerical methods used for solving these systems, the Milstein method, the Simplified Second-Order Taylor Scheme, and the Stochastic Runge-Kutta (SRK) method, have been compared. The Kubo oscillator model has been considered and the stochastic dynamics of this model have been solved using numerical methods. Initially, the general structure of SDEs is introduced, and the theoretical foundations of the methods used for solving these systems are explained. In the study, the stochastic model of the Kubo oscillator was solved numerically using the Milstein method, the Simplified Second-Order Taylor Scheme, and the SRK method. The results obtained were compared with exact solutions. In the numerical computations, the accuracy of all three methods is analyzed for different discretization counts and the results were supported by graphs and error tables. The comparisons revealed that the Simplified Second-Order Taylor Scheme provided more accurate solutions compared to the Milstein method. It is observed that the Taylor method and the SRK 2-stage method gave close results. Additionally, it was observed that increasing the number of discretizations brought both methods closer to the exact solution.