Differential and Integral Equations
- Differential Integral Equations
- Volume 28, Number 3/4 (2015), 221-238.
Resonant time steps and instabilities in the numerical integration of Schrödinger equations
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.
Differential Integral Equations, Volume 28, Number 3/4 (2015), 221-238.
First available in Project Euclid: 4 February 2015
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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