Bibliographic Metadata

Numerical integration of nonlinear evolution equations / von Daniel Haberlik
Additional Titles
Numerische Integration nichtlinearer Evolutionsgleichungen
AuthorHaberlik, Daniel
Thesis advisorAuzinger, Winfried
PublishedWien, 2018
Description65 Seiten
Institutional NoteTechnische Universität Wien, Diplomarbeit, 2018
Arbeit an der Bibliothek noch nicht eingelangt - Daten nicht geprueft
Document typeThesis (Diplom)
Keywords (DE)Einschrittverfahren / Differentialgleichungen / lokale Fehlerschätzung
Keywords (EN)one-step integrator / differential equations / local error estimation
URNurn:nbn:at:at-ubtuw:1-119521 Persistent Identifier (URN)
 The work is publicly available
Numerical integration of nonlinear evolution equations [0.63 mb]
Abstract (English)

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.

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