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Mathematical Problems in Engineering
Volume 2012 (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.

Linked References

  1. J. Bebernes and D. Eberly, Mathematical Problems from Combustion Theory, vol. 83 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1989.
  2. S. Kaplan, “On the growth of solutions of quasi-linear parabolic equations,” Communications on Pure and Applied Mathematics, vol. 16, pp. 305–330, 1963. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. H. Brunner, X. Wu, and J. Zhang, “Computational solution of blow-up problems for semilinear parabolic PDEs on unbounded domains,” SIAM Journal on Scientific Computing, vol. 31, no. 6, pp. 4478–4496, 2009/10. View at Publisher · View at Google Scholar
  4. A. M. Stuart and M. S. Floater, “On the computation of blow-up,” European Journal of Applied Mathematics, vol. 1, no. 1, pp. 47–71, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. C. Bandle and H. Brunner, “Blowup in diffusion equations: a survey,” Journal of Computational and Applied Mathematics, vol. 97, no. 1-2, pp. 3–22, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. C. J. Budd, W. Huang, and R. D. Russell, “Moving mesh methods for problems with blow-up,” SIAM Journal on Scientific Computing, vol. 17, no. 2, pp. 305–327, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. W. Huang, J. Ma, and R. D. Russell, “A study of moving mesh PDE methods for numerical simulation of blowup in reaction diffusion equations,” Journal of Computational Physics, vol. 227, no. 13, pp. 6532–6552, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. J. Ma, Y. Jiang, and K. Xiang, “Numerical simulation of blowup in nonlocal reaction-diffusion equations using a moving mesh method,” Journal of Computational and Applied Mathematics, vol. 230, no. 1, pp. 8–21, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. J. Ma, Y. Jiang, and K. Xiang, “On a moving mesh method for solving partial integro-differential equations,” Journal of Computational Mathematics, vol. 27, no. 6, pp. 713–728, 2009. View at Google Scholar · View at Zentralblatt MATH
  10. J. Chen, Numerical Study of Blowup Problems and Conservation Laws with Moving Mesh Methods, 1996, http://ir.lib.sfu.ca/handle/1892/8368.
  11. H. Brunner, Collocation Methods for Volterra Integral and Related Functional Differential Equations, vol. 15 of Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, Cambridge, UK, 2004. View at Publisher · View at Google Scholar