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Runge-Kutta Lawson schemes for stochastic differential equations. (English) Zbl 07349675
Summary: In this paper, we present a framework to construct general stochastic Runge-Kutta Lawson schemes. We prove that the schemes inherit the consistency and convergence properties of the underlying Runge-Kutta scheme, and confirm this in some numerical experiments. We also investigate the stability properties of the methods and show for some examples, that the new schemes have improved stability properties compared to the underlying schemes.

MSC:
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
65L20 Stability and convergence of numerical methods for ordinary differential equations
93E15 Stochastic stability in control theory
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