A General Class of One-Step Approximation for Index-1 Stochastic Delay-Differential-Algebraic Equations
Year: 2019
Author: Tingting Qin, Chengjian Zhang
Journal of Computational Mathematics, Vol. 37 (2019), Iss. 2 : pp. 151–169
Abstract
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 $θ$-methods, split-step $θ$-methods are proposed, and their strong convergence results are given. Numerical experiments further illustrate the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1711-m2016-0810
Journal of Computational Mathematics, Vol. 37 (2019), Iss. 2 : pp. 151–169
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Stochastic delay differential-algebraic equations One-step discretization schemes Strong convergence.