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Runge-Kutta Methods with Equation Dependent Coefficients

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Numerical Analysis and Its Applications (NAA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8236))

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Abstract

The simplest two and three stage explicit Runge-Kutta methods are examined by a conveniently adapted form of the exponential fitting approach. The unusual feature is that the coefficients of the new versions are no longer constant, as in standard versions, but depend on the equation to be solved. Some valuable properties emerge from this. Thus, in the case of three-stage versions, although in general the order is three, that is the same as for the standard method, this is easily increased to four by a suitable choice of the position of the stage abscissas. Also, the stability properties are massively enhanced. Two particular versions of order four are A-stable, a fact which is quite unusual for explicit methods. This recommends them as efficient tools for solving stiff differential equations.

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Author information

Authors and Affiliations

  1. Department of Theoretical Physics, “Horia Hulubei” National Institute of Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest, Romania

    L. Gr. Ixaru

  2. Academy of Romanian Scientists, 54 Splaiul Independenţei, 050094, Bucharest, Romania

    L. Gr. Ixaru

Authors
  1. L. Gr. Ixaru
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Editor information

Editors and Affiliations

  1. Institute of Information and Communication Technlogies, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl25A, 1113, Sofia, Bulgaria

    Ivan Dimov

  2. Department of Applied Analysis, Pázm\’{a}ny P\’{e}ter s\’{e}t\’{a}ny 1/C,, Eötvös Loránd University, 1117, Budapest, Hungary

    István Faragó

  3. University of Rousse, 8 Studentska Str.,, 7017, Rousse, Bulgaria

    Lubin Vulkov

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Ixaru, L.G. (2013). Runge-Kutta Methods with Equation Dependent Coefficients. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2012. Lecture Notes in Computer Science, vol 8236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41515-9_36

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  • DOI: https://doi.org/10.1007/978-3-642-41515-9_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41514-2

  • Online ISBN: 978-3-642-41515-9

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