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

  • Higinio RamosEmail author
Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI, volume 18)


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.


Error analysis Stability analysis Falkner implicit methods Direct integration methods Second-order initial-value problems Predictor-corrector modes 



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


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Grupo de Computación CientíficaUniversidad de Salamanca, Escuela Politécnica Superior de ZamoraZamoraSpain

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