• An improved local error estimator for symmetric time-stepping schemes

  • We propose a symmetrized version of the defect to be used in the estimation of the local time-stepping error of symmetric one-step methods for the time propagation of linear autonomous evolution equations. Using the anticommutator of the numerical flow and the right-hand side operator in the definition of the defect of the numerical approximation, a local error estimator is obtained which has higher accuracy asymptotically than an established version using the common defect. This theoretical result is illustrated for a splitting method applied to a linear Schrödinger equation.

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  • http://phaidra.univie.ac.at/o:717623

  • Wissenschaftlicher Artikel

  • Angenommene Version

  • 2018

  • 82

  • 106-110

  • Elsevier BV

  • Englisch

  • Embargo

  • 01.09.2020

  • P 30819-N32 – Fonds zur Förderung der wissenschaftlichen Forschung (FWF)

  • MA14-02 – Wiener Wissenschafts-, Forschungs- und Technologiefonds (WWTF)

  • 0893-9659

  • Dewey Dezimal Klassifikation → Naturwissenschaften und Mathematik → Mathematik → Numerical analysis