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Mathematical Problems in Engineering
Volume 2012, Article ID 162034, 15 pages
http://dx.doi.org/10.1155/2012/162034
Research Article

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

Department of Mathematics, University of Johannesburg, Cnr Siemert & Beit Streets, Doornfontein 2028, South Africa

Received 31 August 2011; Revised 8 November 2011; Accepted 8 November 2011

Academic Editor: Robertt A. Fontes Valente

Copyright © 2012 P. G. Dlamini and M. Khumalo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.