Skip to main content Accessibility help
×
Home

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

  • MICHAEL ROBINSON (a1)

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

References

Hide All
[1]Holmes, M. H.. Introduction to Perturbation Methods. Springer, New York, 1995.
[2]Hubbard, J. H. and West, B. H.. Differential Equations: A Dynamical Systems Approach. Springer, Berlin, 1997.
[3]Lee, J. M.. Introduction to Smooth Manifolds. Springer, New York, 2003.
[4]Ważewski, T.. Sur un principe topologique de l’examen de l’allure asymptotique des intégrales des équations différentielles ordinaires. Ann. Soc. Polon. Math. 20 (1947), 279313.

Related content

Powered by UNSILO

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

  • MICHAEL ROBINSON (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.