Fractional-Step Runge-Kutta Methods: Representation and Linear Stability Analysis

@article{Spiteri2022FractionalStepRM,
  title={Fractional-Step Runge-Kutta Methods: Representation and Linear Stability Analysis},
  author={Raymond J. Spiteri and Siqi Wei},
  journal={ArXiv},
  year={2022},
  volume={abs/2205.06365}
}
Fractional-step methods are a popular and powerful divide-and-conquer approach for the numerical solution of differential equations. When the integrators of the fractional steps are Runge–Kutta methods, such methods can be written as generalized additive Runge–Kutta (GARK) methods, and thus the representation and analysis of such methods can be done through the GARK framework. We show how the general Butcher tableau representation and linear stability of such methods are related to the coef… 

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