Mathematics of Computation

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

Author(s): Christian Lubich.
Journal: Math. Comp. 77 (2008), 2141-2153.
MSC (2000): Primary 65M15
Posted: February 19, 2008
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Abstract: We give an error analysis of Strang-type splitting integrators for nonlinear Schrödinger equations. For Schrödinger-Poisson equations with an

-regular solution, a first-order error bound in the

norm is shown and used to derive a second-order error bound in the

norm. For the cubic Schrödinger equation with an

-regular solution, first-order convergence in the

norm is used to obtain second-order convergence in the

norm. Basic tools in the error analysis are Lie-commutator bounds for estimating the local error and

-conditional stability for error propagation, where

for the Schrödinger-Poisson system and

for the cubic Schrödinger equation.

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Christian Lubich
Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
Email: lubich@na.uni-tuebingen.de

DOI: 10.1090/S0025-5718-08-02101-7
PII: S 0025-5718(08)02101-7
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
Posted: February 19, 2008
Additional Notes: This work was supported by DFG, SFB 382.
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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