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

Advances in Difference Equations

Bo Liu¹  Fengnan Liu¹  Xiaopeng Zhao² 

[1] College of Mathematics, Jilin University, Changchun, China;School of Science, Jiangnan University, Wuxi, China

关键词: extended Fisher-Kolmogorov equation;    Fourier pseudo-spectral method;    stability;    convergence;    error estimate;   

DOI  :  10.1186/s13662-017-1154-x

学科分类：数学（综合）

来源: SpringerOpen

【 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.

【 授权许可】

CC BY