Title: Numerische Integration nichtlinearer Evolutionsgleichungen : Entwicklung und Implementierung verschiedener numerischer Verfahren
Other Titles: Numerical integration of nonlinear evolution equations
Language: English
Authors: Haberlik, Daniel 
Qualification level: Diploma
Keywords: Einschrittverfahren; Differentialgleichungen; lokale Fehlerschätzung
one-step integrator; differential equations; local error estimation
Advisor: Auzinger, Winfried 
Issue Date: 2018
Number of Pages: 65
Qualification level: Diploma
This diploma thesis deals with the analysis and the numerical implementation of integration schemes for evolution equations, as well as asymptotically correct defect-based local error estimators. Recent work in [Auzinger, Koch, Hofstätter (2018)] introduced the symmetrized defect for the linear, autonomous Schrödinger-type evolution equation, which proved to be of a higher asymptotical order than the well known classical defect, in the case of symmetric time-stepping. In [Auzinger, Koch (2018)] this result was proven to hold true also for nonlinear and nonautonomous evolution equations. In this thesis we recapitulate these results in a concise, but complete manner, whereby we set citations in a more general then detailed way. After that, we apply them to established, as well as newly constructed splitting schemes. To provide numerical verification of the theory, we consider several linear/nonlinear, autonomous/nonautonomous model problems.
URI: https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:1-119521
Library ID: AC15243590
Organisation: E101 - Institut für Analysis und Scientific Computing 
Publication Type: Thesis
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