On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations
By Christian Lubich. Mathematics of Computation, 2008
345 citations recorded by the source corpus.
We give an error analysis of Strang-type splitting integrators for nonlinear Schrodinger equations. For Schrodinger-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 Schrodinger 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 Schrodinger-Poisson system and m = 2 for the cubic Schrodinger equation.
Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/32faeed5c9070e727b6e387150a32c6ab2ed40eb
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In Computational Mechanics
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Citations in the corpus
- Mathematical Models and Numerical Methods for Bose-Einstein Condensation (2012, methodology): “Similar to [139], one can compute the commutator [T̂ , V̂ ](ψ) = T̂ ′(ψ)V̂ (ψ)− V̂ ′(ψ)T̂ (ψ)”