On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations
Christian Lubich
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Source: Crossref
Published: Feb 19, 2008
DOI: 10.1090/s0025-5718-08-02101-7
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We give an error analysis of Strang-type splitting integrators for nonlinear Schrödinger equations. For Schrödinger-Poisson equations with an H 4 H^4 -regular solution, a first-order error bound in the H 1 H^1 norm is shown and used to derive a second-order error bound in the L 2 L_2 norm. For the cubic Schrödinger equation with an H 4 H^4 -regular solution, first-order convergence in the H 2 H^2 norm is used to obtain second-order convergence in the L 2 L_2 norm. Basic tools in the error analysis are Lie-commutator bounds for estimating the local error and H m H^m -conditional stability for error propagation, where m = 1 m=1 for the Schrödinger-Poisson system and m = 2 m=2 for the cubic Schrödinger equation.
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