Volume 37, Issue 2
A General Class of One-Step Approximation for Index-1 Stochastic Delay-Differential-Algebraic Equations

Tingting Qin & Chengjian Zhang

J. Comp. Math., 37 (2019), pp. 151-169.

Published online: 2018-09

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  • 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.

  • Keywords

Stochastic delay differential-algebraic equations, One-step discretization schemes, Strong convergence.

  • AMS Subject Headings

34K50, 60H35, 65L80, 65L20.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

tingtingqin@mail.hust.edu.cn (Tingting Qin)

cjzhang@hust.edu.cn (Chengjian Zhang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-37-151, author = {Qin , Tingting and Zhang , Chengjian }, title = {A General Class of One-Step Approximation for Index-1 Stochastic Delay-Differential-Algebraic Equations}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {37}, number = {2}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1711-m2016-0810}, url = {http://global-sci.org/intro/article_detail/jcm/12673.html} }
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 -

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.

Tingting Qin & Chengjian Zhang. (2019). A General Class of One-Step Approximation for Index-1 Stochastic Delay-Differential-Algebraic Equations. Journal of Computational Mathematics. 37 (2). 151-169. doi:10.4208/jcm.1711-m2016-0810
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