### A GENERAL CLASS OF ONE-STEP APPROXIMATION FOR INDEX-1 STOCHASTIC DELAY-DIFFERENTIAL-ALGEBRAIC EQUATIONS

Tingting Qin1,2, Chengjian Zhang1,2

1. 1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China;
2. Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China
• Received:2016-12-12 Revised:2017-04-28 Online:2019-03-15 Published:2019-03-15
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The authors would like to thank the anonymous referees for their valuable comments and helpful suggestions. The first author Tingting Qin is supported by Fundamental Research Funds for the Central Universities (Grant No. HUST:2016YXMS009) and the second author Chengjian Zhang (corresponding author) is supported by NSFC (Grant No. 11571128).

Tingting Qin, Chengjian Zhang. A GENERAL CLASS OF ONE-STEP APPROXIMATION FOR INDEX-1 STOCHASTIC DELAY-DIFFERENTIAL-ALGEBRAIC EQUATIONS[J]. Journal of Computational Mathematics, 2019, 37(2): 151-169.

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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