Numerische Mathematik

, Volume 97, Issue 3, pp 537-554

First online:

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

  • Ken’ichiro TanakaAffiliated withDepartment of Mathematical Informatics, Graduate School of Information Science and Technology Email author 
  • , Sunao MurashigeAffiliated withDepartment of Complexity Science and Engineering, Graduate School of Frontier Sciences
  • , Shin’ichi OishiAffiliated withDepartment of Computer Science, School of Science and Engineering

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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.