Model order reduction for nonlinear Schrodinger equation

KARASÖZEN, BÜLENT; Akkoyunlu, Canan; Uzunca, Murat

doi:10.1016/j.amc.2015.02.001

Model order reduction for nonlinear Schrodinger equation

KARASÖZEN B., Akkoyunlu C., Uzunca M.

APPLIED MATHEMATICS AND COMPUTATION, cilt.258, ss.509-519, 2015 (SCI-Expanded, Scopus)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 258
Basım Tarihi: 2015
Doi Numarası: 10.1016/j.amc.2015.02.001
Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sayfa Sayıları: ss.509-519
Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

We apply the proper orthogonal decomposition (POD) to the nonlinear Schrodinger (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. (C) 2015 Elsevier Inc. All rights reserved.