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Oscillation of Runge-Kutta Methods for a Scalar Differential Equation with One Delay

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Information Computing and Applications (ICICA 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 307))

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Abstract

Numerical oscillation of Runge-Kutta methods for differential equations with piecewise constant arguments is considered in this paper. The conditions of oscillation for the Runge-Kutta methods are obtained. It is proven that the numerical oscillation on the integer nodes are equivalent to the numerical oscillation on the any nodes and oscillation of the analytic solution is preserved by the Runge-Kutta methods. Moreover, the relationship between stability and oscillation is discussed for analytic solution and numerical solution, respectively. At last, several numerical simulations are carried out to support the theoretical analysis of the research.

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Author information

Authors and Affiliations

  1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou, 510006, China

    Qi Wang & Jiechang Wen

  2. School of Environmental Science and Engineering, Guangdong University of Technology, Guangzhou, 510006, China

    Fenglian Fu

Authors
  1. Qi Wang
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  2. Jiechang Wen
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  3. Fenglian Fu
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Editor information

Editors and Affiliations

  1. College of Sciences, Hebei United University, 063000, Tangshan, Hebei, China

    Chunfeng Liu  & Aimin Yang  & 

  2. Northeastern University at Qinhuangdao, Hebei, China

    Leizhen Wang

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© 2012 Springer-Verlag Berlin Heidelberg

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Wang, Q., Wen, J., Fu, F. (2012). Oscillation of Runge-Kutta Methods for a Scalar Differential Equation with One Delay. In: Liu, C., Wang, L., Yang, A. (eds) Information Computing and Applications. ICICA 2012. Communications in Computer and Information Science, vol 307. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34038-3_46

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  • DOI: https://doi.org/10.1007/978-3-642-34038-3_46

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34037-6

  • Online ISBN: 978-3-642-34038-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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