On a Large Time-Stepping Method for the Swift-Hohenberg Equation (Advances in Applied Mathematics and Mechanics, 2021)
The main purpose of this work is to contrast and analyze a large time-steppingnumerical method for the Swift-Hohenberg (SH) equation. This model requiresvery large time simulation to reach steady state, so developing a large time stepalgorithm becomes necessary to improve the computational efficiency. In this paper,a semi-implicit Euler scheme in time is adopted. An extra artificial term is added tothe discretized system in order to preserve the energy stability unconditionally. Thestability property is proved rigorously based on an energy approach. Numerical experimentsare used to demonstrate the effectiveness of the large time-stepping approachesby comparing with the classical scheme.