TY - JOUR
T1 - Strong Converge Order of the General One-Step Method for Neutral Stochastic Delay Differential Equations under a Global Monotone Condition
AU - Yue , Chao
AU - Zhuang , Haoyong
AU - Zhao , Longbin
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1654
EP - 1681
PY - 2025
DA - 2025/09
SN - 17
DO - http://doi.org/10.4208/aamm.OA-2024-0017
UR - https://global-sci.org/intro/article_detail/aamm/24490.html
KW - Strong convergence, general one-step method, C-stability, B-consistency, neutral stochastic delay differential equations.
AB - <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>