@Article{JMS-48-4,
author = {Zhang, Jun and Wu-Lan, Li and Xin-Yue, Fan and Yu, Xiao-Jun},
title = {Numerical Approximations of the Spectral Discretization of Flame Front Model},
journal = {Journal of Mathematical Study},
year = {2015},
volume = {48},
number = {4},
pages = {345--361},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v48n4.15.03},
url = {https://global-sci.com/article/87835/numerical-approximations-of-the-spectral-discretization-of-flame-front-model}
}