The Energy Stable Sixth-Order Implicit-Explicit Scheme with Scalar Auxiliary Variable Method for the Swift-Hohenberg Equation
Abstract
In the present work, we propose two kinds of sixth-order numerical scheme for the Swift-Hohenberg (SH) equation. We adopt the implicit-explicit sixth-order scheme (BDF6) combined with the generalized scalar auxiliary variable (GSAV) method for temporal discretization and the Fourier spectral approach for spatial discretization. We rigorously prove the energy dissipation law of our proposed scheme and the $H^2$ norm error analysis. Furthermore, we promote the corresponding numerical scheme with the exponential scalar auxiliary variable (ESAV) method, which satisfies energy dissipation law. Finally, we show the substantial examples that verify the energy dissipation property and convergence of the two schemes.
Fields of Study & Subjects
Numerical methods for differential equations
Advanced Numerical Methods in Computational Mathematics
Matrix Theory and Algorithms
Publication details
- Journal / source
- International Journal of Numerical Analysis and Modeling
- Publisher
- Global Science Press
- Volume
- 23
- Issue
- 4
- Pages
- 461–479
- Publication date
- 29 May 2026