| Abstract: |
| In this talk, we develop 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 $\theta$-methods, split-step $\theta$-methods are proposed, and their strong convergence results are given. Numerical experiments further illustrate the theoretical results. |
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