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- W2964341192 abstract "In this paper, we present the Stroboscopic Averaging Method (SAM), recently introduced in [7,8,10,13], which aims at numerically solving highly-oscillatory differential equations. More specifically, we first apply SAM to the Schrödinger equation on the $1$-dimensional torus and on the real line with harmonic potential, with the aim of assessing its efficiency: as compared to the well-established standard splitting schemes, the stiffer the problem is, the larger the speed-up grows (up to a factor $100$ in our tests). The geometric properties of SAM are also explored: on very long time intervals, symmetric implementations of the method show a very good preservation of the mass invariant and of the energy. In a second series of experiments on $2$-dimensional equations, we demonstrate the ability of SAM to capture qualitatively the long-time evolution of the solution (without spurring high oscillations)." @default.
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- W2964341192 date "2016-10-01" @default.
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- W2964341192 title "Solving highly-oscillatory NLS with SAM: Numerical efficiency and long-time behavior" @default.
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- W2964341192 doi "https://doi.org/10.3934/dcdss.2016053" @default.
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