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A Study of (m,k)-Methods for Solving Differential-Algebraic Systems of Index 1

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Book cover Mathematical Modeling of Technological Processes (CITech 2015)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 549))

Abstract

A class (m,k)-methods is discussed for the numerical solution of the initial value problems for implicit systems of ordinary differential equations. The order conditions and convergence of the numerical solution in the case of implementation of the scheme with the time-lagging of matrices derivatives for systems of index 1 are obtained. At \(k\le 4\) the order conditions are studied and schemes optimal computing costs are obtained.

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Author information

Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, Academy of Sciences, Siberian Branch, pr. Ak. Lavrent’eva 6, Akademgorodok, 630090, Novosibirsk, Russia

    Alexander I. Levykin

  2. Institute of Computational Modeling, Academy of Sciences, Siberian Branch, Akademgorodok 50, Str. 4, 660036, Krasnoyarsk, Russia

    Eugeny A. Novikov

Authors
  1. Alexander I. Levykin
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  2. Eugeny A. Novikov
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Corresponding author

Correspondence to Eugeny A. Novikov .

Editor information

Editors and Affiliations

  1. Al-Farabi Kazakh National University, Almaty, Kazakhstan

    Nargozy Danaev

  2. Novosibirsk, Russia

    Yurii Shokin

  3. National University, Almaty, Kazakhstan

    Akhmed-Zaki Darkhan

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© 2015 Springer International Publishing Switzerland

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Levykin, A.I., Novikov, E.A. (2015). A Study of (m,k)-Methods for Solving Differential-Algebraic Systems of Index 1. In: Danaev, N., Shokin, Y., Darkhan, AZ. (eds) Mathematical Modeling of Technological Processes. CITech 2015. Communications in Computer and Information Science, vol 549. Springer, Cham. https://doi.org/10.1007/978-3-319-25058-8_10

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  • DOI: https://doi.org/10.1007/978-3-319-25058-8_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25057-1

  • Online ISBN: 978-3-319-25058-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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