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

Ken'ichiro Tanaka, Sunao Murashige, Shinichi Oishi

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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.

Original language English 537-554 18 Numerische Mathematik 97 3 https://doi.org/10.1007/s00211-003-0515-4 Published - 2004 May

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Numerical Verification
Extended Systems
Turning Point
Necessary Conditions
Sufficient Conditions
Verify
Banach Fixed Point Theorem
Nonlinear systems
Uniqueness
Nonlinear Systems

ASJC Scopus subject areas

• Mathematics(all)
• Applied Mathematics
• Computational Mathematics

Cite this

On necessary and sufficient conditions for numerical verification of double turning points. / Tanaka, Ken'ichiro; Murashige, Sunao; Oishi, Shinichi.

In: Numerische Mathematik, Vol. 97, No. 3, 05.2004, p. 537-554.

Research output: Contribution to journalArticle

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