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Time-integration methods for a dispersion-managed nonlinear Schrödinger equation

Mikl, Marcel

Modeling dispersion-managed optical fibers leads to a nonlinear Schrödinger equation where the linear part is multiplied by a rapidly changing piecewise constant coefficient function. Typically, the occurring oscillations of the solution and the discontinuous coefficients impose severe problems for traditional time-integrators. In this thesis, we present and analyze tailor-made numerical methods for this equation which attain a desired accuracy with significantly larger step-sizes than traditional methods. The construction of the methods is based on a favorable transformation of problem and the explicit computation of certain integrals over highly oscillatory phases. In the error analysis, we deviate from the classical concept “stability and consistency yield convergence”. Instead, we utilize recursion formulas for the global error to exploit cancellation effects of various oscillatory error terms allowing us to prove higher accuracy for special step-sizes.

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DOI: 10.5445/IR/1000071577
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Publikationstyp Hochschulschrift
Publikationsjahr 2017
Sprache Englisch
Identifikator urn:nbn:de:swb:90-715776
KITopen-ID: 1000071577
Verlag Karlsruher Institut für Technologie (KIT)
Umfang IV, 146 S.
Art der Arbeit Dissertation
Fakultät Fakultät für Mathematik (MATH)
Institut Institut für Angewandte und Numerische Mathematik (IANM)
Prüfungsdatum 28.06.2017
Referent/Betreuer Prof. T. Jahnke
Projektinformation GRK 1294/2 (DFG, DFG KOORD, GRK 1294/2)
SFB 1173/1 (DFG, DFG KOORD, SFB 1173/1 2015)
Schlagwörter dispersion management, nonlinear Schödinger equation, highly oscillatory problem, discontinuous coefficients, adiabatic integrator, error bounds, limit dynamics
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