TY - JOUR
T1 - Numerical Approximations of the Spectral Discretization of Flame Front Model
AU - Zhang , Jun
AU - Li , Wu-Lan
AU - Fan , Xin-Yue
AU - Yu , Xiao-Jun
JO - Journal of Mathematical Study
VL - 4
SP - 345
EP - 361
PY - 2015
DA - 2015/12
SN - 48
DO - http://doi.org/10.4208/jms.v48n4.15.03
UR - https://global-sci.org/intro/article_detail/jms/9939.html
KW - Flame front equation, Finite difference, Fourier method, Error estimates.
AB - <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>