Journal article
THE NEWTON–RAPHSON METHOD AND ADAPTIVE ODE SOLVERS
- SCHNEEBELI, HANS RUDOLF Kantonsschule, CH-5400 Baden, Switzerland
- WIHLER, THOMAS P. Mathematics Institute, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland
- 2011-11-20
Published in:
- Fractals. - World Scientific Pub Co Pte Lt. - 2011, vol. 19, no. 01, p. 87-99
English
The Newton–Raphson method for solving nonlinear equations f(x) = 0 in ℝn is discussed within the context of ordinary differential equations. This framework makes it possible to reformulate the scheme by means of an adaptive step size control procedure that aims at reducing the chaotic behavior of the original method without losing the quadratic convergence close to the roots. The performance of the modified scheme is illustrated with a few low-dimensional examples.
- Language
-
- English
- Open access status
- closed
- Identifiers
-
- DOI 10.1142/s0218348x11005191
- ISSN 0218-348X
- Persistent URL
- https://folia.unifr.ch/global/documents/244496
Statistics
Document views: 17
File downloads: