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.
KeywordsNonlinear System Point Theorem Additional Condition Turning Point Fixed Point Theorem
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- 1.Kanzawa, Y., Oishi, S.: Calculating bifurcation points with guaranteed accuracy. IEICE Trans. Fundamentals E82-A~6, 1055–1061 (1999)Google Scholar
- 2.Kuznetsov, Y.A.: Elements of Applied Bifurcation Theory. Second Edition, Springer-Verlag, New York, 1998Google Scholar
- 4.Oishi, S.: Introduction to Nonlinear Analysis. Corona-sha, Tokyo, 1997 [in Japanese]Google Scholar
- 7.Tanaka, K.: Computer-assisted existence proof of the bifurcation points of Duffing’s equation. Batchelor thesis of the Department of Mathematical Engineering, Faculty of Engineering, the University of Tokyo, 2002 [in Japanese]Google Scholar
- 8.Yang, Z.-H., Keller, H.B.: A direct method for computing higher order folds. SIAM J. Sci. Stat. Comput. 7, 351–361 (1986)Google Scholar
- 9.Zeidler, E.: Nonlinear Functional Analysis and its Applications I – Fixed-Point Theorems. Springer, New York, 1986Google Scholar
- 10.Zeidler, E.: Applied Functional Analysis – Main Principles and Their Applications. Applications to Mathematical Sciences 109, Springer, New York, 1995Google Scholar