Abstract
Using Newton’s method to compute solu-tions of a discrete boundary value problem amounts to iterating a certain map in HRN, and solutions appear as attractors of the dynamical system thus defined. This note is an experimental study of the global properties of the basins of attraction for these attractors. Particular interest is in a comparison with fundamental properties of Julia sets for rational functions in the complex plane.
Research was partially supported by ‘Stiftung Volkswagenwerk’
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Peitgen, HO., Prüfer, M. (1984). Global Aspects of Newton’s Method for Nonlinear Boundary Value Problems. In: Küpper, T., Mittelmann, H.D., Weber, H. (eds) Numerical Methods for Bifurcation Problems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 70. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6256-1_25
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DOI: https://doi.org/10.1007/978-3-0348-6256-1_25
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