Model order reduction for nonlinear Schrodinger equation

作者：Karasozen Bolent^*; Akkoyunlu Canan; Uzunca Murat

来源：Applied Mathematics and Computation, 2015, 258: 509-519.

DOI：10.1016/j.amc.2015.02.001

• Nonlinear Schrodinger equation
• Proper orthogonal decomposition
• Model order reduction
• Error analysis

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.

• 出版日期2015-5-1