TY - JOUR
T1 - A General Class of One-Step Approximation for Index-1 Stochastic Delay-Differential-Algebraic Equations
AU - Qin , Tingting
AU - Zhang , Chengjian
JO - Journal of Computational Mathematics
VL - 2
SP - 151
EP - 169
PY - 2018
DA - 2018/09
SN - 37
DO - http://doi.org/10.4208/jcm.1711-m2016-0810
UR - https://global-sci.org/intro/article_detail/jcm/12673.html
KW - Stochastic delay differential-algebraic equations, One-step discretization schemes, Strong convergence.
AB - <p style="text-align: justify;">This paper develops a class of general one-step discretization methods for solving the
index-1 stochastic delay differential-algebraic equations. The existence and uniqueness
theorem of strong solutions of index-1 equations is given. A strong convergence criterion
of the methods is derived, which is applicable to a series of one-step stochastic numerical
methods. Some specific numerical methods, such as the Euler-Maruyama method, stochastic&nbsp; $θ$-methods, split-step $θ$-methods are proposed, and their strong convergence results are
given. Numerical experiments further illustrate the theoretical results.</p>