Finite difference approximation for nonlinear Schrödinger equations with application to blow-up computation

This paper presents a coherent analysis of the finite difference method to nonlinear Schrödinger (NLS) equations in one spatial dimension. We use the discrete H 1 framework to establish well-posedness and error estimates in the L ∞ norm. The nonlinearity f ( u ) of a NLS equation is assumed to satis...

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Veröffentlicht in:	Japan journal of industrial and applied mathematics 2016-07, Vol.33 (2), p.427-470
Hauptverfasser:	Saito, Norikazu, Sasaki, Takiko
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics Computation Computational Mathematics and Numerical Analysis Convergence Discretization Finite difference method Mathematics Mathematics and Statistics Nonlinear equations Nonlinearity Original Paper Schrodinger equation Well posed problems
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