Year: 2015
Author: Jun Zhang, Wu-Lan Li, Xin-Yue Fan, Xiao-Jun Yu
Journal of Mathematical Study, Vol. 48 (2015), Iss. 4 : pp. 345–361
Abstract
In this paper, we consider the numerical solution of the flame front equation, which is one of the most fundamental equations for modeling combustion theory. A schema combining a finite difference approach in the time direction and a spectral method for the space discretization is proposed. We give a detailed analysis for the proposed schema by providing some stability and error estimates in a particular case. For the general case, although we are unable to provide a rigorous proof for the stability, some numerical experiments are carried out to verify the efficiency of the schema. Our numerical results show that the stable solution manifolds have a simple structure when $\beta$ is small, while they become more complex as the bifurcation parameter $\beta$ increases. At last numerical experiments were performed to support the claim the solution of flame front equation preserves the same structure as K-S equation.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v48n4.15.03
Journal of Mathematical Study, Vol. 48 (2015), Iss. 4 : pp. 345–361
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Flame front equation Finite difference Fourier method Error estimates.