TY - JOUR
T1 - A semi-analytical Fourier spectral method for the Swift–Hohenberg equation
AU - Lee, Hyun Geun
N1 - Publisher Copyright:
© 2017 Elsevier Ltd
PY - 2017/10/15
Y1 - 2017/10/15
N2 - 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.
AB - 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.
KW - First- and second-order convergence
KW - Fourier spectral method
KW - Operator splitting method
KW - Swift–Hohenberg equation
UR - http://www.scopus.com/inward/record.url?scp=85026740388&partnerID=8YFLogxK
U2 - 10.1016/j.camwa.2017.06.053
DO - 10.1016/j.camwa.2017.06.053
M3 - Article
AN - SCOPUS:85026740388
SN - 0898-1221
VL - 74
SP - 1885
EP - 1896
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
IS - 8
ER -