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Sequential eigenfunction expansion for a problem in combustion theory

Published online by Cambridge University Press:  17 February 2009

M. Al-Refai  and
K. K. Tam
M. Al-Refai
Affiliation:
Department of Mathematics and Statistics, McGill University, Burnside Hall, Room 1005, 805 Sherbrooke St. West, Monterals, Quebec H3A 2K5, Canada; e-mail: [email protected].
K. K. Tam
Affiliation:
Department of Mathematics and Statistics, McGill University, Burnside Hall, Room 1005, 805 Sherbrooke St. West, Monterals, Quebec H3A 2K5, Canada; e-mail: [email protected].
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Abstract

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A method of sequential eigenfunction expansion is developed for a semi-linear parabolic equation. It allows the time-dependent coefficients of the eigenfunctions to be determined sequentially and iterated to reach convergence. At any stage, only a single ordinary differential equation needs to be considered, in contrast to the Galerkin method which requires the consideration of a system of equations. The method is applied to a central problemin combustion theory to provide a definitive answer to the question of the influence of the initial data in determining whether the solution is sub- or super-critical, in the case of multiple steady-state solutions. It is expected this method will prove useful in dealing with similar problems.

Type
Research Article
Information
The ANZIAM Journal , Volume 45 , Issue 1 , July 2003 , pp. 35 - 48
Copyright
Copyright © Australian Mathematical Society 2003

References

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