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March/April 2015 Resonant time steps and instabilities in the numerical integration of Schrödinger equations
Erwan Faou, Tiphaine Jézéquel
Differential Integral Equations 28(3/4): 221-238 (March/April 2015).

Abstract

We consider the linear and nonlinear cubic Schrödinger equations with periodic boundary conditions and their approximations by splitting methods. We prove that for a dense set of arbitrarily small time steps, there exist numerical solutions leading to strong numerical instabilities, preventing the energy conservation and regularity bounds obtained for the exact solution. We analyze rigorously these instabilities in the semi-discrete and fully discrete cases.

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Erwan Faou. Tiphaine Jézéquel. "Resonant time steps and instabilities in the numerical integration of Schrödinger equations." Differential Integral Equations 28 (3/4) 221 - 238, March/April 2015.

Information

Published: March/April 2015
First available in Project Euclid: 4 February 2015

zbMATH: 1363.37038
MathSciNet: MR3306560

Subjects:
Primary: 35B34, 37M15, 65P40

Rights: Copyright © 2015 Khayyam Publishing, Inc.

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Vol.28 • No. 3/4 • March/April 2015
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