## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Numerical simulations of the energy-stable scheme for Swift-Hohenberg equation

**ABSTRACT**

A collocation Fourier scheme for Swift-Hohenberg equation based on the convex splitting idea is implemented. To ensure an efficient numerical computation, we propose a general framework with linear iteration algorithm to solve the nonlinear coupled equations which arise with the semi-implicit scheme. Following the contraction mapping theorem, we present a detailed convergence analysis for the linear iteration algorithm. Various numerical simulations, including verification of accuracy, dissipative property of discrete energy and pattern formation, are presented to demonstrate the efficiency and the robustness of proposed method.

**KEYWORDS**

PAPER SUBMITTED: 2018-05-15

PAPER REVISED: 2018-09-20

PAPER ACCEPTED: 2018-11-15

PUBLISHED ONLINE: 2019-03-31

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