Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations

Author: Christian Lubich
Journal: Math. Comp. 77 (2008), 2141-2153
MSC (2000): Primary 65M15
Published electronically: February 19, 2008
MathSciNet review: 2429878
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give an error analysis of Strang-type splitting integrators for nonlinear Schrödinger equations. For Schrödinger-Poisson equations with an $ H^4$-regular solution, a first-order error bound in the $ H^1$ norm is shown and used to derive a second-order error bound in the $ L_2$ norm. For the cubic Schrödinger equation with an $ H^4$-regular solution, first-order convergence in the $ H^2$ norm is used to obtain second-order convergence in the $ L_2$ norm. Basic tools in the error analysis are Lie-commutator bounds for estimating the local error and $ H^m$-conditional stability for error propagation, where $ m=1$ for the Schrödinger-Poisson system and $ m=2$ for the cubic Schrödinger equation.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 65M15

Retrieve articles in all journals with MSC (2000): 65M15

Additional Information

Christian Lubich
Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany

Keywords: Split-step method, split-operator scheme, semilinear Schr\"odinger equations, error analysis, stability, regularity
Received by editor(s): January 9, 2007
Received by editor(s) in revised form: September 12, 2007
Published electronically: February 19, 2008
Additional Notes: This work was supported by DFG, SFB 382.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.