Skip to main content
×
Home
    • Aa
    • Aa
  • Ergodic Theory and Dynamical Systems, Volume 29, Issue 1
  • February 2009, pp. 223-253

An asymptotic-numerical approach for examining global solutions to an ordinary differential equation

  • MICHAEL ROBINSON (a1)
  • DOI: http://dx.doi.org/10.1017/S0143385708080061
  • Published online: 01 February 2009
Abstract
Abstract

Purely numerical methods do not always provide an accurate way to find all the global solutions to nonlinear ordinary differential equations on infinite intervals. For example, finite-difference methods fail to capture the asymptotic behavior of solutions, which might be critical for ensuring global existence. We first show, by way of a detailed example, how asymptotic information alone provides significant insight into the structure of global solutions to a nonlinear ordinary differential equation. Then we propose a method for providing this missing asymptotic data to a numerical solver, and show how the combined approach provides more detailed results than either method alone.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]M. H. Holmes . Introduction to Perturbation Methods. Springer, New York, 1995.

[3]J. M. Lee . Introduction to Smooth Manifolds. Springer, New York, 2003.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax