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.