A Stabilized Second Order Exponential Time Differencing Multistep Method for Thin Film Growth Model Without Slope Selection


In this paper, a stabilized second order in time accurate linear exponential time differencing (ETD) scheme for the no-slope-selection thin film growth model is presented. an artificial stabilizing term $ A{\tau}^2\frac{\mathrm{\partial}{\Delta}^2u}{\mathrm{\partial}t}$ is added to the physical model to achieve energy stability, with ETD-Based multi-step approximations and Fourier collocation spectral method applied in the time integral and spatial discretization of the evolution equation, respectively. Long time energy stability and detailed o ∞(0,T;o 2) error analysis are provided based on the energy method, with a careful estimate of the aliasing error. in addition, numerical experiments are presented to demonstrate the energy decay and convergence rate.


Mathematics and Statistics

Keywords and Phrases

Convergence Analysis; Epitaxial Thin Film Growth; Exponential Time Differencing; Long Time Energy Stability; Second Order Scheme

International Standard Serial Number (ISSN)

2804-7214; 2822-7840

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2023 The Authors, All rights reserved.

Creative Commons Licensing

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Publication Date

01 May 2020