Runge-Kutta Characterization of the Generalized Summation-by-Parts Approach in Time

@inproceedings{Boom2014RungeKuttaCO,
  title={Runge-Kutta Characterization of the Generalized Summation-by-Parts Approach in Time},
  author={Pieter D. Boom and David W. Zingg},
  year={2014}
}
This article extends the theory of dual-consistent summation-by-parts (SBP) and generalized SBP (GSBP) time-marching methods by showing that they are implicit Runge-Kutta schemes. Through this connection, the accuracy theory for the pointwise solution, as well as the solution projected to the end of each time step, is extended for nonlinear problems. Furthermore, it is shown that these minimum guaranteed order results can be superseded by leveraging the full nonlinear order conditions of Runge… CONTINUE READING

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