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A new multistep method with optimized characteristics for initial and/or boundary value problems

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Abstract

In this paper we introduce, for the first time in the literature, an optimized multistage symmetric two-step method. This method is considered as optimized due to the following reasons: (1) it is of tenth-algebraic order scheme, (2) it has obliterated the phase-lag and its first, second, third and fourth derivatives, (3) it has improved stability characteristics, (4) it is a P-stable method. For the new proposed multistage symmetric two-step method we present a full theoretical investigation consisted of: (1) local truncation error and comparative error analysis, (2) stability analysis and (3) interval of periodicity analysis. The effectiveness of the new builded multistage symmetric two-step method is evaluated on the solution of systems of coupled differential equations of the Schrödinger type.

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Authors and Affiliations

  1. School of Electronics and Information Engineering, Fuqing Branch of Fujian Normal University, Fuqing, 350300, People’s Republic of China

    Guo-Hua Qiu

  2. Department of Computer Science and Technology, Neusoft Institute of Guangdong, Foshan, 528228, China

    Chenglian Liu

  3. Department of Mathematics, College of Sciences, King Saud University, P. O. Box 2455, Riyadh, 11451, Saudi Arabia

    T. E. Simos

  4. Group of Modern Computational Methods, Ural Federal University, 19 Mira Street, Ekaterinburg, Russian Federation, 620002

    T. E. Simos

  5. Department of Automation Engineering, TEI of Sterea Hellas, Psachna Campus, 34400, Psachna, Greece

    T. E. Simos

  6. Section of Mathematics, Department of Civil Engineering, Democritus University of Thrace, Xanthi, Greece

    T. E. Simos

  7. 10 Konitsis Street, Amphithea - Paleon Faliron, 175 64, Athens, Greece

    T. E. Simos

Authors
  1. Guo-Hua Qiu
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  2. Chenglian Liu
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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 (http://isihighlycited.com/), Active Member of the European Academy of Sciences and Arts. Active Member of the European Academy of Sciences. Corresponding Member of European Academy of Arts, Sciences and Humanities.

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Qiu, GH., Liu, C. & Simos, T.E. A new multistep method with optimized characteristics for initial and/or boundary value problems. J Math Chem 57, 119–148 (2019). https://doi.org/10.1007/s10910-018-0940-3

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  • DOI: https://doi.org/10.1007/s10910-018-0940-3

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