Fourier pseudo-spectral method for the extended Fisher-Kolmogorov equation in two dimensions

被引：15
|
作者：
Liu, Fengnan [1 ]
Zhao, Xiaopeng [2 ]
Liu, Bo [1 ]
机构：
[1] Jilin Univ, Coll Math, Qianjin St, Changchun 130012, Peoples R China
[2] Jiangnan Univ, Sch Sci, Lihu Rd, Wuxi 214122, Peoples R China
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2017年
关键词：
extended Fisher-Kolmogorov equation; Fourier pseudo-spectral method; stability; convergence; error estimate; VELOCITY SELECTION; MARGINAL STABILITY; PROPAGATION; DIFFUSION;
D O I：
10.1186/s13662-017-1154-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the study of pattern formation in bi-stable systems, the extended Fisher-Kolmogorov (EFK) equation plays an important role. In this paper, a Fourier pseudo-spectral method for solving the EFK equation in two space dimensions is presented. Prior bounds are proved using Lyapunov function. Further, optimal error estimates are established for the semi-discrete scheme. Finally, a fully discrete scheme based on Crank-Nicolson method is proposed, and related optimal error estimates are derived and some numerical experiments are presented.
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收藏
页数：17
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