Symbolic Manipulation of Flows of Nonlinear Evolution Equations, with Application in the Analysis of Split-Step Time Integrators

  • Winfried Auzinger
  • Harald Hofstätter
  • Othmar Koch
Conference paper

DOI: 10.1007/978-3-319-45641-6_4

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9890)
Cite this paper as:
Auzinger W., Hofstätter H., Koch O. (2016) Symbolic Manipulation of Flows of Nonlinear Evolution Equations, with Application in the Analysis of Split-Step Time Integrators. In: Gerdt V., Koepf W., Seiler W., Vorozhtsov E. (eds) Computer Algebra in Scientific Computing. CASC 2016. Lecture Notes in Computer Science, vol 9890. Springer, Cham

Abstract

We describe a package realized in the Julia programming language which performs symbolic manipulations applied to nonlinear evolution equations, their flows, and commutators of such objects. This tool was employed to perform contrived computations arising in the analysis of the local error of operator splitting methods. It enabled the proof of the convergence of the basic method and of the asymptotical correctness of a defect-based error estimator. The performance of our package is illustrated on several examples.

Keywords

Nonlinear evolution equations Time integration Splitting methods Symbolic computation Julia language 

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Winfried Auzinger
    • 1
  • Harald Hofstätter
    • 1
  • Othmar Koch
    • 2
  1. 1.Technische Universität WienViennaAustria
  2. 2.Universität WienViennaAustria

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