• Defect-based local error estimators for splitting methods, with application to Schrödinger equations, Part II. Higher-order methods for linear problems

  • In this work, defect-based local error estimators for higher-order exponential operator splitting methods are constructed and analyzed in the context of time-dependent linear Schrödinger equations. The technically involved procedure is carried out in detail for a general three-stage third-order splitting method and then extended to the higher-order case. Asymptotical correctness of the a posteriori local error estimator is proven under natural commutator bounds for the involved operators, and along the way the known (non)stiff order conditions and a priori convergence bounds are recovered. The theoretical error estimates for higher-order splitting methods are confirmed by numerical examples for a test problem of Schrödinger type. Further numerical experiments for a test problem of parabolic type complement the investigations.

  • PDF

  • http://phaidra.univie.ac.at/o:423906

  • Wissenschaftlicher Artikel

  • Angenommene Version

  • 01.01.2014

  • 255

  • 384-403

  • Elsevier BV

  • Englisch

  • Frei zugänglich

  • 02.01.2016

  • P24157-N13 – Fonds zur Förderung der wissenschaftlichen Forschung (FWF)

  • 0377-0427

  • Linear evolution equations; Time-dependent linear Schrödinger equations; Time integration; Higher-order exponential operator splitting methods; Defect correction; A priori local error estimates; A posteriori local error estimates

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