A-stability of Runge-Kutta methods for systems with additive noise

@article{Hernandez1992AstabilityOR,
  title={A-stability of Runge-Kutta methods for systems with additive noise},
  author={Diego Bricio Hernandez and Renato Spigler},
  journal={BIT Numerical Mathematics},
  year={1992},
  volume={32},
  pages={620-633}
}
Numerical stability of both explicit and implicit Runge-Kutta methods for solving ordinary differential equations with an additive noise term is studied. The concept of numerical stability of deterministic schemes is extended to the stochastic case, and a stochastic analogue of Dahlquist'sA-stability is proposed. It is shown that the discretization of the drift term alone controls theA-stability of the whole scheme. The quantitative effect of implicitness uponA-stability is also investigated… CONTINUE READING

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