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On the Dynamics of Shooting Methods for solving Sturm-Liouville Problems

Limber, Martha N. and Curry, James H. (1994) On the Dynamics of Shooting Methods for solving Sturm-Liouville Problems. [Preprint]

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      Abstract

      It is shown that simple shooting and a standard iterative technique, e.g. Newton's method, applied to a regular elliptic Sturm-Liouville boundary value problem form a chaotic dynamical system. We then develop and apply an action-angle modification of the Prufer substitution based on a Hamiltonian formalism which, when applied to the transformed Sturm-Liouville system, eliminates the chaotic set and ensures convergence of the Newton iterates. A further generalization of the Prufer modified transformation leads to a class of higher order heuristic methods for integrating Sturm-Liouville equations.

      Item Type: Preprint
      Additional Information: pubdom FALSE
      Subjects: 65-xx Numerical analysis > 65Lxx Ordinary differential equations
      34-xx Ordinary differential equations > 34Bxx Boundary value problems
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 16 Nov 2003
      Last Modified: 21 Apr 2010 11:13
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/72

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