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Two optimized symmetric eight-step implicit methods for initial-value problems with oscillating solutions

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Abstract

In this paper, we present two optimized eight-step symmetric implicit methods with phase-lag order ten and infinite (phase-fitted). The methods are constructed to solve numerically the radial time-independent Schrödinger equation with the use of the Woods–Saxon potential. They can also be used to integrate related IVPs with oscillating solutions such as orbital problems. We compare the two new methods to some recently constructed optimized methods from the literature. We measure the efficiency of the methods and conclude that the new method with infinite order of phase-lag is the most efficient of all the compared methods and for all the problems solved.

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Authors and Affiliations

  1. Laboratory of Computer Sciences, Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese, 22 100, Tripolis, Greece

    G. A. Panopoulos, Z. A. Anastassi & T. E. Simos

  2. 26 Menelaou Street, Amfithea—Paleon Faliron, 175 64, Athens, Greece

    T. E. Simos

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  1. G. A. Panopoulos
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  2. Z. A. Anastassi
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  3. T. E. Simos
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Correspondence to T. E. Simos.

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T. E. Simos—Highly Cited Researcher, Active Member of the European Academy of Sciences and Arts.

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Panopoulos, G.A., Anastassi, Z.A. & Simos, T.E. Two optimized symmetric eight-step implicit methods for initial-value problems with oscillating solutions. J Math Chem 46, 604–620 (2009). https://doi.org/10.1007/s10910-008-9506-0

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  • DOI: https://doi.org/10.1007/s10910-008-9506-0

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