Global aspects of Newton’s method for nonlinear boundary value problems. (English) Zbl 0539.65059

Peitgen, Heinz-Otto; Prüfer, Michael

Numerical methods for bifurcation problems, Proc. Conf., Dortmund/Ger. 1983, ISNM 70, 352-368 (1984).

Summary: [For the entire collection see Zbl 0535.00021.]
Using Newton’s method to compute solutions of a discrete boundary value problem amounts to iterating a certain map in \({\mathbb{R}}^ N\), 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.

MSC:

65L10	Numerical solution of boundary value problems involving ordinary differential equations
65H10	Numerical computation of solutions to systems of equations
34B15	Nonlinear boundary value problems for ordinary differential equations

Keywords:

Newton’s method; attractors; dynamical system; experimental study; comparison; Julia sets

Citations:

Zbl 0535.00021