• Defect-based local error estimators for high-order splitting methods involving three linear operators

  • Prior work on high-order exponential operator splitting methods is extended to evolution equations defined by three linear operators. A posteriori local error estimators are constructed via a suitable integral representation of the local error involving the defect associated with the splitting solution and quadrature approximation via Hermite interpolation. In order to prove asymptotical correctness, a multiple integral representation involving iterated defects is deduced by repeated application of the variation-of-constant formula. The error analysis within the framework of abstract evolution equations provides the basis for concrete applications. Numerical examples for initial-boundary value problems of Schrödinger and of parabolic type confirm the asymptotical correctness of the proposed a posteriori error estimators.

  • PDF

  • http://phaidra.univie.ac.at/o:423891

  • Article

  • Accepted Version

  • Numerical Algorithms

  • 06.11.2014

  • 70

  • 1

  • 61-91

  • Springer

  • English

  • Open access

  • 07.11.2015

  • P24157-N13 – Austrian Science Fund (FWF)

  • 1017-1398

  • Linear evolution equations; Time integration methods; High-order exponential operator splitting methods; Local error; A posteriori local error estimators

  • Dewey Decimal Classification → Science → Mathematics → Numerical analysis