Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-12-02T20:41:59.254Z Has data issue: false hasContentIssue false
  • English
  • Français

On the numerical solution of the diffusion equation subject to the specification of mass

Published online by Cambridge University Press:  17 February 2009

A. B. Gumel
A. B. Gumel
Affiliation:
Faculty of Information Technology, University Telekom, 75450 Melaka, Malaysia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A parallel algorithm is developed for the numerical solution of the diffusion equation ut = uxx, 0 < x < t < T, subject to u(x, 0) = f(x), ux(X, t) = g(t) and the specification of mass .

Type
Research Article
Information
The ANZIAM Journal , Volume 40 , Issue 4 , April 1999 , pp. 475 - 483
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Cannon, J. R. and van der Hoek, J., “The existence of and a continuous dependence result for the solution of the heat equation subject to the specification of energy”, Suppl. Bolletino Unione Mat. Ital. 1 (1981) 253–282.Google Scholar
[2]Cannon, J. R., Esteva, S. P. and van der Hoek, J., “A Galerkin procedure for the diffusion equation subject to the specification of mass”, SIAM J. Numer. Anal. 24 (1987) 499–515.Google Scholar
[3]Cannon, J. R., Lin, Yanping and Wang, Shingmin, “An implicit finite difference scheme for the diffusion equation subject to mass specification”, Int. J. Engng. Sci. 28 (7) (1990) 573–578.Google Scholar
[4]Gumel, A. B., “Parallel and sequential algorithms for parabolic equations with applications”, (PhD Thesis, Brunei University, 1993).Google Scholar
[5]Gumel, A. B., Twizell, E. H. and Arigu, M. A., “Parallel L 0-stable methods for multi-dimensional heat equation”, Parallel Algorithms and Applications 11 (1997) 13–25.Google Scholar
[6]Lambert, J. D., Numerical methods for ordinary differential systems: The initial-value problem (John Wiley and Sons, Chichester, 1991).Google Scholar
[7]Lawson, J. D., “Some numerical methods for stiff ordinary and partial differential equations”, Second Manitoba Conf. on Numerical Mathematics, Winnipeg, Canada (1972) 27–34.Google Scholar
[8]Padé, M. H., “Sur la répresentation approcheé d'une fonction par des fractions rationelles”, Ann. de l'Ecole Normale Supérieure 9 (suppl) (1982).Google Scholar
[9]Swayne, D. A., “Time-dependent boundary and interior forcing in locally one-dimensional schemes”, S1AMJ. Sci. Stat. Comput. 8 (1987) 755–767.CrossRefGoogle Scholar
[10]Twizell, E. H., Numerical methods, with applications in the biomedical sciences (Ellis Horwood, Chichester, and John Wiley, New York, 1988).Google Scholar
[11]Twizell, E. H., Khaliq, A. Q. M. and Voss, D. A., “Sequential and parallel algorithms for second-order initial-value problems”, WSSIA A 2 (1993) 399–412.Google Scholar