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Numerical analysis of quasiperiodic solutions to nonlinear differential equations

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Abstract

The paper first generalizes the definition of exponential dichotomy and gives another simple proof of Urabe’s Existence Theorem to nonlinear quasiperiodic differential equations. Next, a useful numerical analysis of quasiperiodic solutions to second order differential equations is presented. The paper extends the results given in previous papers [3], [9], [16] which dealt with weakly nonlinear differential equations. A few examples of numerical analysis of Van der Pol type equations are illustrated.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Engineering, Tokushima University, 770, Tokushima, Japan

    Yoshitane Shinohara

  2. Department of Computer Science, Faculty of Engineering, University of Yamanashi, 400, Kofu, Japan

    Mitsunobu Kurihara

  3. Department of Mathematics, Faculty of Engineering, Tokushima University, 770, Tokushima, Japan

    Atsuhito Kohda

Authors
  1. Yoshitane Shinohara
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  2. Mitsunobu Kurihara
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  3. Atsuhito Kohda
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Shinohara, Y., Kurihara, M. & Kohda, A. Numerical analysis of quasiperiodic solutions to nonlinear differential equations. Japan J. Appl. Math. 3, 315–330 (1986). https://doi.org/10.1007/BF03167105

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  • DOI: https://doi.org/10.1007/BF03167105

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