Fourier pseudo-spectral method for the extended Fisher-Kolmogorov equation in two dimensions
نویسندگان
چکیده
*Correspondence: [email protected] 2School of Science, Jiangnan University, Lihu Road, Wuxi, 214122, China Full list of author information is available at the end of the article Abstract 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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