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On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations. (English) Zbl 1198.65186
Summary: 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.

##### MSC:
 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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