@Article{AAMM-17-1654,
author = {Yue , ChaoZhuang , Haoyong and Zhao , Longbin},
title = {Strong Converge Order of the General One-Step Method for Neutral Stochastic Delay Differential Equations under a Global Monotone Condition},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2025},
volume = {17},
number = {6},
pages = {1654--1681},
abstract = {<p style="text-align: justify;">We study the strong convergence of the general one-step method for neutral
 stochastic delay differential equations with a variable delay. First, we give the notions
 of C-stability and B-consistency, and then establish a fundamental theorem of strong
 convergence for the general one-step method solving the nonlinear neutral stochastic
 delay differential equations, where the corresponding diffusion coefficient with respect
 to the non-delay variables is highly nonlinear. Then, we construct the split-step backward Euler method which is a special implicit one-step method, and prove that it is
 C-stable, B-consistent, and strongly convergent of order 1/2. Finally, we give some
 numerical experiments to support the obtained results.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2024-0017},
url = {http://global-sci.org/intro/article_detail/aamm/24490.html}
}