Title
Symbolic Manipulation of Flows of Nonlinear Evolution Equations, with Application in the Analysis of Split-Step Time Integrators
Author
Winfried Auzinger
Technische Universität Wien
Author
Harald Hofstätter
Technische Universität Wien
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 equationstime integrationsplitting methodssymbolic computationJulia language
Object type
Language
English [eng]
Persistent identifier
https://phaidra.univie.ac.at/o:502372
Is contained in
Title
Computer Algebra in Scientific Computing
18th International Workshop, CASC 2016
Editor
Vladimir P. Gerdt
Wolfram Koepf
Werner M. Seiler
Evgenii V. Vorozhtsov
Series
Title
Lecture Notes in Computer Science
Volume
9890
From page
43
To page
57
Publisher
Springer Nature
Version type
Date available
2017-09-09
Date accepted
2016
Access rights

Download

University of Vienna | Universitätsring 1 | 1010 Vienna | T +43-1-4277-0