Stochastic Runge-Kutta methods for multi-dimensional Ito stochastic differential algebraic equations

In this paper, we discuss the numerical solutions to index 1 stochastic differential algebraic equations. We introduce a new class of weak second-order stochastic Runge-Kutta methods for finding the numerical approximate solutions to multi-dimensional stochastic differential algebraic equations. A four-stage stiffly accurate stochastic Runge-Kutta methods for approximating analytical solutions to index 1 stochastic differential algebraic equations are derived. By colored rooted tree analysis, the order conditions for the stochastic Runge-Kutta methods of order two satisfying the weak convergence is obtained. The scalar test equations are considered to obtain the mean-square stability and the T-stability of weak second-order stochastic Runge-Kutta methods. Finally, some numerical illustrations are provided to prove the theoretical findings. (C) 2021 The Authors. Published by Elsevier B.V.