On the Computation of Blow-up Solutions for Semilinear ODEs and Parabolic PDEs

We introduce an adaptive numerical method for computing blow-up solutions for ODEs and well-known reaction-diffusion equations. The method is based on the implicit midpoint method and the implicit Euler method. We demonstrate that the method produces superior results to the adaptive PECE-implicit me...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical Problems in Engineering 2012-01, Vol.2012 (2012), p.532-546-034
Main Authors: Dlamini, P. G., Khumalo, Melusi
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We introduce an adaptive numerical method for computing blow-up solutions for ODEs and well-known reaction-diffusion equations. The method is based on the implicit midpoint method and the implicit Euler method. We demonstrate that the method produces superior results to the adaptive PECE-implicit method and the MATLAB solver of comparable order.
ISSN:1024-123X
1563-5147
DOI:10.1155/2012/162034