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A hybrid method with phase-lag and derivatives equal to zero for the numerical integration of the Schrödinger equation

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Abstract

A family of hybrid methods with algebraic order eight is proposed, with phase-lag and its first four derivatives eliminated. We investigate the behavior of the new algorithm and the property of the local truncation error and a comparison with other methods leads to conclusions and remarks about its accuracy and stability. The newly created method, as well as another Numerov-type methods, are applied to the resonance problem of the radial Schrödinger equation. The eigenenergies approximations, which are obtained prove the superiority of the new two-step method.

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Abbreviations

LTE:

Local Truncation Error

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

    A. Konguetsof

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    A. Konguetsof

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Konguetsof, A. A hybrid method with phase-lag and derivatives equal to zero for the numerical integration of the Schrödinger equation. J Math Chem 49, 1330–1356 (2011). https://doi.org/10.1007/s10910-011-9824-5

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