Model order reduction for nonlinear Schrödinger equation

Bülent Karasözen, Canan Akkoyunlu and Murat Uzunca

Applied Mathematics and Computation, 2015, vol. 258, issue C, 509-519

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.

Keywords: Nonlinear Schrödinger equation; Proper orthogonal decomposition; Model order reduction; Error analysis (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:258:y:2015:i:c:p:509-519

DOI: 10.1016/j.amc.2015.02.001

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