Sequential eigenfunction expansion for a problem in combustion theory

M. Al-Refai, K. K. Tam

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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 problem in 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.

Original languageEnglish
Pages (from-to)35-48
Number of pages14
JournalANZIAM Journal
Issue number1
Publication statusPublished - Jul 2003
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (miscellaneous)


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