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Formulation and Analysis of a Class of Direct Implicit Integration Methods for Special Second-Order I.V.P.s in Predictor-Corrector Modes

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Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 18))

Abstract

A detailed analysis of different formulations of a class of explicit direct integration methods in predictor-corrector modes for solving special second-order initial-value problems has been carried out (Comput. Phys. Comm. 181 (2010) 1833–1841), showing that the adequate combination of the involved formulas led to an increase in the order of the method. In this paper we consider different formulations of the implicit direct integration methods in predictor-corrector modes. An analysis of the accumulated truncation errors is made and the stability analysis is addressed, including the intervals of stability. Some numerical examples are presented to show the performance of the different formulations. These methods may constitute a reliable alternative to other methods in the literature for solving special second order problems.

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Acknowledgement

The author is pleased to acknowledge a referee for carefully reading the manuscript.

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Authors and Affiliations

  1. Grupo de Computación Científica, Universidad de Salamanca, Escuela Politécnica Superior de Zamora, Zamora, Spain

    Higinio Ramos

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  1. Higinio Ramos
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Correspondence to Higinio Ramos .

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Editors and Affiliations

  1. Department of Applied Mathematics and Statistics, Technical University of Cartagena, Cartagena, Murcia, Spain

    Juan Luis García Guirao

  2. Department of Applied Mathematics and Statistics, Technical University of Cartagena, Cartagena, Murcia, Spain

    José Alberto Murillo Hernández

  3. Department of Applied Mathematics and Statistics, Technical University of Cartagena, Cartagena, Murcia, Spain

    Francisco Periago Esparza

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Ramos, H. (2019). Formulation and Analysis of a Class of Direct Implicit Integration Methods for Special Second-Order I.V.P.s in Predictor-Corrector Modes. In: García Guirao, J., Murillo Hernández, J., Periago Esparza, F. (eds) Recent Advances in Differential Equations and Applications. SEMA SIMAI Springer Series, vol 18. Springer, Cham. https://doi.org/10.1007/978-3-030-00341-8_3

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