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.

引用

页数：17

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