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On the Accuracy of Some Absorbing Boundary Conditions for the Schrodinger Equation

    Andrej Bugajev Affiliation
    ; Raimondas Čiegis Affiliation
    ; Rima Kriauzienė Affiliation
    ; Teresė Leonavičienė Affiliation
    ; Julius Žilinskas Affiliation

Abstract

A detailed analysis of absorbing boundary conditions for the linear Schrodinger equation is presented in this paper. It is focused on absorbing boundary conditions that are obtained by using rational functions to approximate the exact transparent boundary conditions. Different strategies are investigated for the optimal selection of the coefficients of these rational functions, including the Pade approximation, the L2 norm approximations of the Fourier symbol, L2 minimization of a reflection coefficient, and two error minimization techniques for the chosen benchmark problems with known exact solutions. The results of computational experiments are given and a detailed comparison of the efficiency of these techniques is presented.

Keyword : finite difference method, nonlocal boundary conditions, approximation, rational functions, Schrodinger equation, absorbing boundary conditions

How to Cite
Bugajev, A., Čiegis, R., Kriauzienė, R., Leonavičienė, T., & Žilinskas, J. (2017). On the Accuracy of Some Absorbing Boundary Conditions for the Schrodinger Equation. Mathematical Modelling and Analysis, 22(3), 408-423. https://doi.org/10.3846/13926292.2017.1306725
Published in Issue
Mar 21, 2017
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