CaltechAUTHORS
  A Caltech Library Service

On the computation of blow-up

Stuart, A. M. and Floater, M. S. (1990) On the computation of blow-up. European Journal of Applied Mathematics, 1 (01). pp. 47-71. ISSN 0956-7925. https://resolver.caltech.edu/CaltechAUTHORS:20170612-101245620

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20170612-101245620

Abstract

Numerical methods for initial-value problems which develop singularities in finite time are analyzed. The objective is to determine simple strategies which produce the correct asymptotic behaviour and give an accurate approximation of the blow-up time. Fixed step methods for scalar ordinary differential equations are studied first and it is shown that there is a natural embedding of the discrete process in a continuous one. This shows clearly how and why the fixed-step strategy fails. A class of time-stepping strategies that correspond to a time- continuous re-scaling of the underlying differential equation is then proposed; this class is analyzed and criteria established to determine suitable choices for the re-scaling. Finally the ideas are applied to a partial differential equation arising from the study of a fluid with temperature-dependent viscosity. The numerical method involves re-formulating the equation as a moving boundary problem for the peak value and applying the ODE time-stepping strategies based on this peak value.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1017/S095679250000005XDOIArticle
http://journals.cambridge.org/abstract_S095679250000005XPublisherArticle
Additional Information:© 1990 Cambridge University Press. Accepted 21 July 1989. M.S.F. was funded by the Science and Engineering Research Council, UK. We are grateful to John Ockendon for interesting us in the problem of blow-up at the boundary.
Funders:
Funding AgencyGrant Number
Science and Engineering Research Council (SERC)UNSPECIFIED
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Andrew StuartJ13
Issue or Number:01
Record Number:CaltechAUTHORS:20170612-101245620
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170612-101245620
Official Citation:A. M. Stuart and M. S. Floater (1990). On the computation of blow-up. European Journal of Applied Mathematics, 1, pp 47-71 doi:10.1017/S095679250000005X
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78097
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:12 Jun 2017 20:40
Last Modified:03 Oct 2019 18:05

Repository Staff Only: item control page