SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Projected explicit Lawson methods for the integration of Schrödinger equation

B. Cano and A. González-Pachón

Abstract
In this talk we will prove that explicit Lawson methods, when projected onto one of the invariants of nonlinear Schrödinger equation (norm) are also automatically projected onto another invariant (momentum) for many solutions. As this procedure is very cheap and geometric because two invariants are conserved, we will show that it offers an efficient tool to integrate some solutions of this equation till long times. On the other hand, we will show a detailed study on the numerical performance of these methods against splitting ones, with fixed and variable stepsize implementation.

Bibliography
[1] B. Cano and A. González-Pachón, Projected explicit Lawson methods for the integration of Schrödinger equation, available at http://www.mac.cie.uva.es/ bego/, submitted for publication.

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