International Workshop on Computer Algebra in Scientific Computing

CASC 2016: Computer Algebra in Scientific Computing pp 43-57

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

Volume 9890 of the book series Lecture Notes in Computer Science (LNCS)
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