Combined Method for Solving of 1D Nonlinear Schrödinger Equation

  • Vyacheslav A. TrofimovEmail author
  • Evgeny M. Trykin
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 307)


We propose combined method, based on using of both the conservative finite-difference scheme and non-conservative Rosenbrock method, for solving a linear or non-linear 1D Schrödinger equation. The computer simulation results, obtained by using of combined method, are compared with corresponding results obtained using the conservative finite-difference scheme or Rosenbrock method. For 2D nonlinear problem the proposed method can significantly increase a computer simulation performance due to eliminating of using an iterative process, which is necessary for the conservative finite-difference scheme realization. The efficiency of this combined method with artificial boundary conditions is demonstrated by numerical experiments.


Rosenbrock method Conservative finite-difference scheme Schrödinger equation Artificial boundary conditions 



This work was supported in part by the Russian Foundation for Basic Research under Grant 12-01-00682-a.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Faculty of Computational Mathematics and CyberneticsLomonosov Moscow State UniversityMoscowRussian Federation

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