Resonant time steps and instabilities in the numerical integration of Schrödinger equations - Archive ouverte HAL Access content directly
Journal Articles Differential and integral equations Year : 2015

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

Abstract

We consider the linear and non linear cubic Schrödinger equations with periodic boundary conditions, and their approximations by splitting methods. We prove that for a dense set of arbitrary small time steps, there exists 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.

Dates and versions

hal-00905856 , version 1 (18-11-2013)

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Erwan Faou, Tiphaine Jézéquel. Resonant time steps and instabilities in the numerical integration of Schrödinger equations. Differential and integral equations, 2015, 28 (3-4), pp.221-238. ⟨hal-00905856⟩
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