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Taha, T.R. and Ablowitz, M.J. (1984) Analytical and Numerical Aspects of Certain Nonlinear Evolution Equations. II. Numerical, Nonlinear Schrödinger Equation. Journal of Computational Physics, 55, 203-230.
http://dx.doi.org/10.1016/0021-9991(84)90003-2

has been cited by the following article:

• TITLE: Spline Solution for the Nonlinear Schrödinger Equation

  AUTHORS: Bin Lin

  KEYWORDS: Nonlinear Schrödinger Equation, Exponential Spline Interpolation, Gross-Pitaevskii Equation, Mass and Energy Conservation

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.4 No.8, August 25, 2016

  ABSTRACT: We develop an exponential spline interpolation method to solve the nonlinear Schrödinger equation. The truncation error and stability analysis of the method are investigated and the method is shown to be unconditionally stable. The conservation quantities are computed to determine the conservation properties of the problem. We will describe the method and present numerical tests by two problems. The numerical simulations results demonstrate the well performance of the proposed method.