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Model order reduction for nonlinear Schrödinger equation

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  • Karasözen, Bülent
  • Akkoyunlu, Canan
  • Uzunca, Murat

Abstract

We apply the proper orthogonal decomposition (POD) to the nonlinear Schrödinger (NLS) equation to derive a reduced order model. The NLS equation is discretized in space by finite differences and is solved in time by structure preserving symplectic mid-point rule. A priori error estimates are derived for the POD reduced dynamical system. Numerical results for one and two dimensional NLS equations, coupled NLS equation with soliton solutions show that the low-dimensional approximations obtained by POD reproduce very well the characteristic dynamics of the system, such as preservation of energy and the solutions.

Suggested Citation

  • Karasözen, Bülent & Akkoyunlu, Canan & Uzunca, Murat, 2015. "Model order reduction for nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 509-519.
    • Handle: RePEc:eee:apmaco:v:258:y:2015:i:c:p:509-519
    DOI: 10.1016/j.amc.2015.02.001
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    References listed on IDEAS

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    1. Oliver Lass & Stefan Volkwein, 2014. "Adaptive POD basis computation for parametrized nonlinear systems using optimal snapshot location," Computational Optimization and Applications, Springer, vol. 58(3), pages 645-677, July.
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    Cited by:

    1. Kim, Jin-Gyun & Seo, Jaho & Lim, Jae Hyuk, 2019. "Novel modal methods for transient analysis with a reduced order model based on enhanced Craig–Bampton formulation," Applied Mathematics and Computation, Elsevier, vol. 344, pages 30-45.

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