Computer Algebra in Scientific Computing

Volume 9890 of the series Lecture Notes in Computer Science pp 43-57


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

  • Winfried AuzingerAffiliated withTechnische Universität Wien
  • , Harald HofstätterAffiliated withTechnische Universität Wien Email author 
  • , Othmar KochAffiliated withUniversität Wien

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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.


Nonlinear evolution equations Time integration Splitting methods Symbolic computation Julia language