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Experience-Driven, Method-Agnostic Algorithm for Controlling Numerical Integration of ODE Systems

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Technological Transformation: A New Role For Human, Machines And Management (TT 2020)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 157))

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Abstract

An algorithm is proposed to control the step size and an optional discrete parameter of a single-step numerical integration method for ordinary differential equation (ODE) systems, capable of estimating step local error norm. The proposed algorithm outperforms traditional ones in the case of ODE systems with non-smooth right hand side. Instead of relying on the dependency of local step error on step size, as traditional algorithms do, our algorithm collects discrete statistical data during numerical solution and makes decisions about the step size changes basing on the analysis of that data. In the end, a real-life application example is shown.

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Acknowledgments

Authors are thankful to the Russian Science Foundation for their support of research under grant No. 18-11-00245.

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Authors and Affiliations

  1. Peter the Great St. Petersburg Polytechnic University, Polytechnicheskaya, 29, 195251, St. Petersburg, Russian Federation

    Stepan Orlov

  2. Schaeffler Automotive Buehl GmbH & Co. KG, Industriestraße 3, 77815, Bühl, Germany

    Lidia Burkovski

Authors
  1. Stepan Orlov
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  2. Lidia Burkovski
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Corresponding author

Correspondence to Stepan Orlov .

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Editors and Affiliations

  1. Hamburg University of Technology, Hamburg, Hamburg, Germany

    Hanno Schaumburg

  2. Peter the Great Saint-Petersburg Polytechnic University, St.Petersburg, Russia

    Vadim Korablev

  3. Deutsch Kasachische Universitat, Almaty, Kazakhstan

    Laszlo Ungvari

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Orlov, S., Burkovski, L. (2021). Experience-Driven, Method-Agnostic Algorithm for Controlling Numerical Integration of ODE Systems. In: Schaumburg, H., Korablev, V., Ungvari, L. (eds) Technological Transformation: A New Role For Human, Machines And Management. TT 2020. Lecture Notes in Networks and Systems, vol 157. Springer, Cham. https://doi.org/10.1007/978-3-030-64430-7_10

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