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On necessary and sufficient conditions for numerical verification of double turning points

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This paper describes numerical verification of a double turning point of a nonlinear system using an extended system. To verify the existence of a double turning point, we need to prove that one of the solutions of the extended system corresponds to the double turning point. For that, we propose an extended system with an additional condition. As an example, for a finite dimensional problem, we verify the existence and local uniqueness of a double turning point numerically using the extended system and a verification method based on the Banach fixed point theorem.

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Authors and Affiliations

  1. Department of Mathematical Informatics, Graduate School of Information Science and Technology, the University of Tokyo, Tokyo, 113-8656, Japan

    Ken’ichiro Tanaka

  2. Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, the University of Tokyo, Chiba 277-8561, Japan

    Sunao Murashige

  3. Department of Computer Science, School of Science and Engineering, Waseda University, Tokyo, 169-8555, Japan

    Shin’ichi Oishi

Authors
  1. Ken’ichiro Tanaka
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  2. Sunao Murashige
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  3. Shin’ichi Oishi
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Corresponding author

Correspondence to Ken’ichiro Tanaka.

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Mathematics Subject Classification (2000): 65J15, 65G20, 65P30

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Tanaka, K., Murashige, S. & Oishi, S. On necessary and sufficient conditions for numerical verification of double turning points. Numer. Math. 97, 537–554 (2004). https://doi.org/10.1007/s00211-003-0515-4

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  • DOI: https://doi.org/10.1007/s00211-003-0515-4

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