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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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