A semi-analytical Fourier spectral method for the Swift–Hohenberg equation. (15th October 2017)

• Record Type: Journal Article
• Authors: Lee, Hyun Geun
• Is Part Of: Computers & mathematics with applications. Volume 74:issue 8(2017)
• Page Start: 1885
• Page End: 1896
• Publication Date: 2017-10-15
• Subjects: Swift–Hohenberg equation -- First- and second-order convergence -- Operator splitting method -- Fourier spectral method; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.06.053
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: The Swift–Hohenberg (SH) equation has been widely used as a model for the study of pattern formation. The SH equation is a fourth-order nonlinear partial differential equation and cannot generally be solved analytically. Therefore, computer simulations play an essential role in understanding of nonequilibrium processing. The aim of this paper is to present first- and second-order semi-analytical Fourier spectral methods as an accurate and efficient approach for solving the SH equation. The methods are based on the operator splitting method and are to split the SH equation into linear and nonlinear subequations. The linear and nonlinear subequations have closed-form solutions in the Fourier and physical spaces, respectively. The methods are simple to implement and computationally cheap to achieve high-order time accuracy. Numerical experiments are presented demonstrating the accuracy and efficiency of proposed methods.