The implementation comparison between the Euler and trivial coupling schemes for achieving strong convergence

Abstract

<abstract><p>This study aimed to develop efficient numerical techniques with the same accuracy level as exact solutions of stochastic differential equations (SDEs). The MATLAB program was used to find solutions for the Euler and trivial coupling methods. The results of these methods were then compared and analyzed. The results show that Euler and trivial coupling methods give the same strong convergence. Furthermore, we demonstrated that these methods achieve strong convergence with a standard order of one-half to the exact solution of the SDE. Moreover, the Euler method is characterized by its speed, ease of application and ability to find solutions through computer programs.</p></abstract>