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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations
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by Christian Lubich HTML | PDF
Math. Comp. 77 (2008), 2141-2153 Request permission


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.
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Additional Information
  • Christian Lubich
  • Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
  • MR Author ID: 116445
  • Email:
  • 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.
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 77 (2008), 2141-2153
  • MSC (2000): Primary 65M15
  • DOI:
  • MathSciNet review: 2429878