• Defect-based local error estimators for splitting methods, with application to Schrödinger equations, Part III: The nonlinear case

  • The present work is concerned with the efficient time integration of nonlinear evolution equations by exponential operator splitting methods. Defect-based local error estimators serving as a reliable basis for adaptive stepsize control are constructed and analyzed. In the context of time-dependent nonlinear Schrödinger equations, asymptotical correctness of the local error estimators associated with the first-order Lie-Trotter and second-order Strang splitting methods is proven. Numerical examples confirm the theoretical results and illustrate the performance of adaptive stepsize control.

  • PDF

  • http://phaidra.univie.ac.at/o:423905

  • Wissenschaftlicher Artikel

  • Angenommene Version

  • 2015

  • 273

  • 182-204

  • Elsevier BV

  • Englisch

  • Embargo

  • 02.01.2017

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

  • 0377-0427

  • Nonlinear evolution equations; Time-dependent nonlinear Schrödinger equations; Exponential operator splitting methods; A priori local error analysis; A posteriori local error analysis

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