Constructive Methods for Nonlinear Boundary Value Problems by Dr. Wolf-Jürgen Beyn (auth.), J. Albrecht, L. Collatz, K.

By Dr. Wolf-Jürgen Beyn (auth.), J. Albrecht, L. Collatz, K. Kirchgässner (eds.)

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Additional info for Constructive Methods for Nonlinear Boundary Value Problems and Nonlinear Oscillations: Conference at the Oberwolfach Mathematical Research Institute, Black Forest, November 19–25, 1978

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Dieser Effekt wirkt sich vor allem bei Beispielen unangenehm aus, deren Konvergenzbereich bei Iteration an der Stelle s von s stark abhangt, wo also die Annahme von globalen Fehlerabschatzungen wie (V2) eine zu grobe Vereinfachung darstell. Weitere numerische Beispiele zu (I3PM) finden sich in [3]. 6. Literaturverzeichnis [1] J. H. Avila. The feasibility of continuation methods for nonlinear equations. SIAM J. Numer. , 11 (1974), pp. 102-120. [2] P. Deuflhard. A stepsize control for continuation methods with special application to multiple shooting techniques.

62 einem modifizierten C neu berechnet. Ist die Bedingung bei zwei aufeinanderfolgenden Durchlaufen in der selben Stufe si verletzt, wird der gesamte ProzeB mit einer groBeren unteren Schranke C0 fur C neu gestartet. (d. h. man verlangt eine groBere Genauigkeit der Zwischenlosungen (xi,si)) In allen Fallen wird nach jeder Iteration C neu gesetzt. Abbruch). 5. Numerische Experimente Einige numerische Resultate bei Verwendung von (I3PM) (alle Rechnungen wurden auf einer Anlage IBM 360/44 mit doppelter Genauigkeit durchgeftihrt): Beispiel 1: Rheinboldt[7] (S.

2] P. Deuflhard. A stepsize control for continuation methods with special application to multiple shooting techniques. Preprint no. 7627, TU Mtinchen, 1976, pp. 1-76. [3] J. Hackl, Hj. Wacker, w. Zulehner. On optimal stepsize control for continuation methods. Preprint no. 101, Univ. Linz, 1978, pp. 1-20. [4] H. T. Kung. The complexity of obtaining starting points for solving operator equations by Newton's method. Analytic Computational Complexity, J. F. , Academic Press, New York, 1976, pp. 35-55.

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