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Two-step high order hybrid explicit method for the numerical solution of the Schrödinger equation

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Abstract

In this paper we present a new method for the numerical solution of the time-independent Schrödinger equation for one spatial dimension and related problems. A technique, based on the phase-lag and its derivatives, is used, in order to calculate the parameters of the new Numerov-type algorithm. We study the relation of the local truncation error with the energy of the model of the radial Schrödinger equation and via this investigation we examine how accurate is the new method compared with other well known numerical methods in the literature. We present also the stability analysis of the new method and the relation of the interval of periodicity with the frequency of the test problem and the frequency of the new developed method. We illustrate the accuracy and computational efficiency of the new developed method via numerical examples.

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Abbreviations

LTE:

Local Truncation Error

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  1. 1 Dimokritou Street, 67100, Xanthi, Greece

    A. Konguetsof

  2. Department of Science, School of Technological Applications, Technological Education Institute of Kavala, 65404, Kavala, Greece

    A. Konguetsof

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Konguetsof, A. Two-step high order hybrid explicit method for the numerical solution of the Schrödinger equation. J Math Chem 48, 224–252 (2010). https://doi.org/10.1007/s10910-010-9664-8

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