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WKB-based schemes for the Schrodinger equation in the semi-classical limit
 

Summary: WKB-based schemes for the Schr¨odinger equation
in the semi-classical limit
A. ARNOLD1
, N. BEN ABDALLAH2
and C. NEGULESCU3
1 Institut f¨ur Analysis und Scientific Computing, Technische Universit¨at Wien
Wiedner Hauptstr. 8, A-1040 Wien, Austria
2 Institut de Math´ematiques de Toulouse (UMR CNRS 5219), Universit´e de Toulouse
Universit´e Paul Sabatier, 118, route de Narbonne, F-31062 Toulouse Cedex, France
3 Laboratoire LATP/CMI (UMR CNRS 6632), Universit´e de Provence
39, rue Joliot Curie, F-13453 Marseille Cedex 13, France
e-mail : anton.arnold@tuwien.ac.at ; naoufel@mip.ups-tlse.fr ;
claudia.negulescu@cmi.univ-mrs.fr
Marseille, May 4, 2010
Abstract
An efficient and accurate numerical method is presented for the solution of
highly oscillatory differential equations. While standard methods would require
a very fine grid to resolve the oscillations, the presented approach uses first an
analytic (second order) WKB-type transformation, which filters out the dominant
oscillations. The resulting ODE is much smoother and can hence be discretized

  

Source: Arnold, Anton - Institut für Analysis und Scientific Computing, Technische Universität Wien

 

Collections: Mathematics