Sequential eigenfunction expansion for a problem in combustion theory

• Autores: M. Al-Refai
• Localización: Anziam journal: The Australian & New Zealand industrial and applied mahtematics journal, ISSN 1446-1811, Vol. 45, Nº 1, 2003, págs. 35-48
• Idioma: inglés
• DOI: 10.1017/s1446181100013146
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• Resumen

  • 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.