TY - JOUR
T1 - On necessary and sufficient conditions for numerical verification of double turning points
AU - Tanaka, Ken'ichiro
AU - Murashige, Sunao
AU - Oishi, Shin'ichi
PY - 2004/5/1
Y1 - 2004/5/1
N2 - 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.
AB - 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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U2 - 10.1007/s00211-003-0515-4
DO - 10.1007/s00211-003-0515-4
M3 - Article
AN - SCOPUS:2942593805
SN - 0029-599X
VL - 97
SP - 537
EP - 554
JO - Numerische Mathematik
JF - Numerische Mathematik
IS - 3
ER -