On necessary and sufficient conditions for numerical verification of double turning points Authors
First Online: 25 February 2004 Received: 06 September 2002 Revised: 17 June 2003 DOI:
Cite this article as: Tanaka, K., Murashige, S. & Oishi, S. Numer. Math. (2004) 97: 537. doi:10.1007/s00211-003-0515-4 Summary.
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.
Mathematics Subject Classification (2000): 65J15, 65G20, 65P30 References
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