On a Comparison of Several Numerical Integration Methods for Ordinary Systems of Differential Equations

  • Anatoliy G. Korotchenko
  • Valentina M. SmoryakovaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11974)


The paper considers the numerical integration methods for ordinary systems of differential equations in which the end of the integration interval is a priori undefined but is defined during the integration process instead. Moreover, the calculation of right hand sides of such systems is an expensive procedure. The paper describes a new integration strategy based on an implicit fourth order method. The proposed strategy employs the behavior of obtained solution to control the integration process. In addition, the number of integration nodes selected by the mentioned method is minimal at every fixed interval under the limitations defined by the local error which results from the approximation of system derivatives.


Finite difference formulas Integration strategies Optimal strategy 



The work is financially supported by the Federal Targeted Program for Research and Development in Priority Areas of Development of the Russian Scientific and Technological Complex for 2014–2020 under the contract No. 14.578.21.0246 (unique identifier RFMEFI57817X0246).


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.N.I. Lobachevsky State UniversityNizhni NovgorodRussia

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