Free access
Issue
ESAIM: M2AN
Volume 43, Number 4, July-August 2009
Special issue on Numerical ODEs today
Page(s) 677 - 687
DOI http://dx.doi.org/10.1051/m2an/2009022
Published online 08 July 2009
  1. M.J. Ablowitz and J.F. Ladik, A nonlinear difference scheme and inverse scattering. Studies Appl. Math. 55 (1976) 213–229.
  2. H. Berland, B. Owren and B. Skaflestad, Solving the nonlinear Schrödinger equation using exponential integrators. Model. Ident. Control 27 (2006) 201–218. [CrossRef]
  3. C. Besse, A relaxation scheme for the nonlinear Schrödinger equation. SIAM J. Numer. Anal. 42 (2004) 934–952 (electronic). [CrossRef] [MathSciNet]
  4. E. Celledoni, D. Cohen and B. Owren, Symmetric exponential integrators with an application to the cubic Schrödinger equation. Found. Comput. Math. 8 (2008) 303–317. [CrossRef] [MathSciNet]
  5. A. Durán and J.M. Sanz-Serna, The numerical integration of relative equilibrium solutions. The nonlinear Schrödinger equation. IMA J. Numer. Anal. 20 (2000) 235–261. [CrossRef] [MathSciNet]
  6. Z. Fei, V.M. Pérez-García and L. Vázquez, Numerical simulation of nonlinear Schrödinger systems: a new conservative scheme. Appl. Math. Comput. 71 (1995) 165–177. [CrossRef] [MathSciNet]
  7. E. Hairer, C. Lubich and G. Wanner, Geometric numerical integration, Structure-preserving algorithms for ordinary differential equations, Springer Series in Computational Mathematics 31. Second Edition, Springer-Verlag, Berlin (2006).
  8. A.L. Islas, D.A. Karpeev and C.M. Schober, Geometric integrators for the nonlinear Schrödinger equation. J. Comput. Phys. 173 (2001) 116–148. [CrossRef] [MathSciNet]
  9. T. Matsuo and D. Furihata, Dissipative or conservative finite-difference schemes for complex-valued nonlinear partial differential equations. J. Comput. Phys. 171 (2001) 425–447. [CrossRef] [MathSciNet]
  10. T.R. Taha and J. Ablowitz, Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation. J. Comput. Phys. 55 (1984) 203–230. [CrossRef] [MathSciNet]
  11. J.A.C. Weideman and B.M. Herbst, Split-step methods for the solution of the nonlinear Schrödinger equation. SIAM J. Numer. Anal. 23 (1986) 485–507. [CrossRef] [MathSciNet]

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