High Order Strong Stability Preserving MultiDerivative Implicit and IMEX Runge-Kutta Methods with Asymptotic Preserving Properties

  title={High Order Strong Stability Preserving MultiDerivative Implicit and IMEX Runge-Kutta Methods with Asymptotic Preserving Properties},
  author={Sigal Gottlieb and Zachary J. Grant and Jingwei Hu and Ruiwen Shu},
  journal={SIAM J. Numer. Anal.},
In this work we present a class of high order unconditionally strong stability preserving (SSP) implicit two-derivative Runge–Kutta schemes, and SSP implicit-explicit (IMEX) multiderivative Runge–Kutta schemes where the time-step restriction is independent of the stiff term. The unconditional SSP property for a method of order p > 2 is unique among SSP methods, and depends on a backward-in-time assumption on the derivative of the operator. We show that this backward derivative condition is… 

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