Abstract
The paper is focused on analyzing the linear stability properties of stochastic Runge–Kutta (SRK) methods interpreted as a stochastic perturbation of the corresponding deterministic Runge–Kutta methods. In particular, we give a condition such that deterministic A-stability is automatically inherited by stochastic Runge–Kutta methods as mean-square A-stability. This issue provides classes of mean-square A-stable SRK methods straightforwardly.
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