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.

中文翻译：

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随机微分方程的Runge–Kutta Lawson方案

在本文中，我们提出了一个框架，用于构建一般的随机Runge-Kutta Lawson方案。我们证明了这些方案继承了底层Runge-Kutta方案的一致性和收敛性，并在一些数值实验中证实了这一点。我们还研究了这些方法的稳定性，并举例说明，与基础方案相比，新方案具有改进的稳定性。