Finite difference methods for an AKNS eigenproblem

J.A.C. Weideman and B.M. Herbst

Mathematics and Computers in Simulation (MATCOM), 1997, vol. 43, issue 1, 77-88

Abstract: We consider the numerical solution of the AKNS eigenproblem associated with the nonlinear Schrödinger equation. Four finite difference methods are considered: two standard schemes (forward and central differences), a discretization introduced by Ablowitz and Ladik (1976), and a modified version of the latter scheme. By comparing these methods both numerically and theoretically we show that the modified Ablowitz-Ladik scheme has several desirable features. This includes the property that with a given number of gridpoints it approximates much larger sections of the spectrum than its rivals.

Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:43:y:1997:i:1:p:77-88

DOI: 10.1016/S0378-4754(96)00057-2

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