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An optimized two-step hybrid block method for solving general second order initial-value problems

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Abstract

A new optimized two-step hybrid block method for the numerical integration of general second-order initial value problems is presented. The method considers two intra-step points which are selected adequately in order to optimize the local truncation errors of the main formulas for the solution and the derivative at the final point of the block. The new method is zero-stable and consistent with fifth algebraic order. Numerical experiments used revealed the superiority of the new method for solving this kind of problems, in comparison with methods of similar characteristics in the literature.

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Authors and Affiliations

  1. Grupo de Computacion Cientifica, Universidad de Salamanca, Salamanca, Spain

    Higinio Ramos

  2. Escuela Politécnica Superior de Zamora, University of Salamanca, Salamanca, Spain

    Higinio Ramos

  3. Department of Computer Science and Technology, Technological Educational Institution of Western Macedonia at Kastoria, Kastoria, Greece

    Z. Kalogiratou

  4. Department of International Trade, Technological Educational Institute of Western Macedonia at Kastoria, GR-521 00, Kastoria, Greece

    Th. Monovasilis

  5. Laboratory of Computational Sciences, Department of Informatics and Telecommunications, Faculty of Economy, Management and Informatics, University of Peloponnese, GR-221 00, Tripolis, Greece

    T. E. Simos

  6. Department of Mathematics, College of Sciences, King Saud University, Riyadh, 11451, Saudi Arabia

    T. E. Simos

Authors
  1. Higinio Ramos
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  2. Z. Kalogiratou
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  3. Th. Monovasilis
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  4. T. E. Simos
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Correspondence to T. E. Simos.

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Ramos, H., Kalogiratou, Z., Monovasilis, T. et al. An optimized two-step hybrid block method for solving general second order initial-value problems. Numer Algor 72, 1089–1102 (2016). https://doi.org/10.1007/s11075-015-0081-8

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  • DOI: https://doi.org/10.1007/s11075-015-0081-8

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