A General Class of One-Step Approximation for Index-1 Stochastic Delay-Differential-Algebraic Equations (Journal of Computational Mathematics, 2018)
This paper develops a class of general one-step discretization methods for solving theindex-1 stochastic delay differential-algebraic equations. The existence and uniquenesstheorem of strong solutions of index-1 equations is given. A strong convergence criterionof the methods is derived, which is applicable to a series of one-step stochastic numericalmethods. Some specific numerical methods, such as the Euler-Maruyama method, stochastic  $θ$-methods, split-step $θ$-methods are proposed, and their strong convergence results aregiven. Numerical experiments further illustrate the theoretical results.
Keywords: Stochastic delay differential-algebraic equations; One-step discretization schemes; Strong convergence.