KIT | KIT-Bibliothek | Impressum

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

Mikl, Marcel

Abstract:
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.


Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Publikationstyp Hochschulschrift
Jahr 2017
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000071577
URN: urn:nbn:de:swb:90-715776
KITopen ID: 1000071577
Verlag Karlsruhe
Umfang IV, 146 S.
Abschlussart 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 (DFG, DFG KOORD, GRK 1294/2)
SFB 1173/1 (DFG, DFG KOORD, SFB 1173/1 2015)
Schlagworte dispersion management, nonlinear Schödinger equation, highly oscillatory problem, discontinuous coefficients, adiabatic integrator, error bounds, limit dynamics
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft KITopen Landing Page