@article{Alnafisah2022, 
author = {Yousef Alnafisah},
title = {A new order from the combination of exact coupling and the Euler scheme},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {4},
pages = {6356-6364},
keywords = {exact coupling, stochastic differential equations (SDE), numerical solution of stochastic differential equations, strong convergence, Euler method},
url = {https://www.sciopen.com/article/10.3934/math.2022353},
doi = {10.3934/math.2022353},
abstract = {Davie defined a Levy variant and the combination of single random variables to ensure that the diffusion matrix did not degenerate. The use of the method proposed by Davie, which is a combination of the Euler method and the exact combination, was investigated for applying the degenerate Levy diffusion approach to        (        B          i      k        (  Y  )      )  . We use certain degenerate conditions of diffusion which contribute to order convergence. We also show MATLAB codes to apply the integrated solution to an SDE and observe a convergence behavior. We also evaluate the agreement between the theoretical values and the MATLAB numerical example.}
}