Differential and Integral Equations

Resonant time steps and instabilities in the numerical integration of Schrödinger equations

Erwan Faou and Tiphaine Jézéquel

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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.

Article information

Source
Differential Integral Equations, Volume 28, Number 3/4 (2015), 221-238.

Dates
First available in Project Euclid: 4 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.die/1423055225

Mathematical Reviews number (MathSciNet)
MR3306560

Zentralblatt MATH identifier
1363.37038

Subjects
Primary: 37M15: Symplectic integrators 65P40: Nonlinear stabilities 35B34: Resonances

Citation

Faou, Erwan; Jézéquel, Tiphaine. Resonant time steps and instabilities in the numerical integration of Schrödinger equations. Differential Integral Equations 28 (2015), no. 3/4, 221--238. https://projecteuclid.org/euclid.die/1423055225


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