TY - JOUR
T1 - Stabilized Invariant Energy Quadratization (S-IEQ) Method for the Molecular Beam Epitaxial Model Without Slope Section
AU - Zhang , Hui
AU - Yang , Xiaofeng
AU - Zhang , Jun
JO - International Journal of Numerical Analysis and Modeling
VL - 5
SP - 642
EP - 655
PY - 2021
DA - 2021/08
SN - 18
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/19386.html
KW - Molecular beam epitaxy, linear, second-order, unconditional energy stability.
AB - <p style="text-align: justify;">The design of numerical approaches for the molecular beam epitaxy models has
always been a hot issue in numerical analysis, in which one of the main challenges for algorithm
design is how to establish a high-order time-accurate numerical method with unconditional energy
stability. The numerical method developed in this paper is based on the “stabilized-Invariant
Energy Quadratization” (S-IEQ) approach. Its novelty is that by adding a very simple linear
stabilization term, the difficulty that the original energy potential for the no-slope selection case
is not bounded from below can be easily overcome. Then by using the standard format of the
IEQ method, we can easily obtain a linear, unconditionally energy stable, and second-order time
accurate scheme for solving the system. We further implement various numerical examples to
demonstrate the stability and accuracy of the proposed scheme.</p>