Long time behavior of splitting methods applied to the linear Schrödinger equation

DOI10.1016/j.crma.2006.11.024zbMath1110.65089OpenAlexW2080377816MaRDI QIDQ869445

Guillaume Dujardin, Erwan Faou

Publication date: 2 March 2007

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2006.11.024

zbMATH Keywords

Hamiltoniansplitting methodstime-discretization

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (7)

Improved Uniform Error Bounds on Time-Splitting Methods for the Long-Time Dynamics of the Dirac Equation with Small Potentials ⋮ Spatial resolution of different discretizations over long-time for the Dirac equation with small potentials ⋮ Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations ⋮ Finite difference time domain methods for the Dirac equation coupled with the Chern-Simons gauge field ⋮ Propagation of Gevrey regularity over long times for the fully discrete Lie Trotter splitting scheme applied to the linear Schrödinger equation ⋮ Uniform error bounds of exponential wave integrator methods for the long-time dynamics of the Dirac equation with small potentials ⋮ Mathematical and computational methods for semiclassical Schrödinger equations

Cites Work

• Unnamed Item
• Error bounds for exponential operator splittings
• Normal form and long time analysis of splitting schemes for the linear Schrödinger equation with small potential
• Simulating Hamiltonian Dynamics
• Order Estimates in Time of Splitting Methods for the Nonlinear Schrödinger Equation
• Resonant and Diophantine step sizes in computing invariant tori of Hamiltonian systems

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