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Your search keyword '"Fengnan Liu"' showing total 2 results
Start Over Author "Fengnan Liu" Journal advances in difference equations
2 results on '"Fengnan Liu"'

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

Author

Fengnan Liu, Xiaopeng Zhao, and Bo Liu

Subjects
extended Fisher-Kolmogorov equation, Fourier pseudo-spectral method, stability, convergence, error estimate, Mathematics, QA1-939
Abstract

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.

Published
2017
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2. Fourier spectral method for the modified Swift-Hohenberg equation

Author

Peng Zhang, Bo Liu, Xiaopeng Zhao, Fengnan Liu, and Wenyu Zhang

Subjects
Partial differential equation, Algebra and Number Theory, Inverse scattering transform, Differential equation, Applied Mathematics, Mathematical analysis, Finite difference method, First-order partial differential equation, symbols.namesake, Fourier transform, symbols, Pseudo-spectral method, Spectral method, Analysis, Mathematics
Abstract

In this paper, we consider the Fourier spectral method for numerically solving the modified Swift-Hohenberg equation. The semi-discrete and fully discrete schemes are established. Moreover, the existence, uniqueness and the optimal error bound are also considered.

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