@Article{AAMM-15-1,
author = {Xiaowei, Chen and Xu, Qian and Songhe, Song},
title = {Fourth-Order Structure-Preserving Method for the Conservative Allen-Cahn Equation},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2023},
volume = {15},
number = {1},
pages = {159--181},
abstract = {<p style="text-align: justify;">We propose a class of up to fourth-order maximum-principle-preserving
and mass-conserving schemes for the conservative Allen-Cahn equation equipped with
a non-local Lagrange multiplier. Based on the second-order finite-difference semi-discretization in the spatial direction, the integrating factor Runge-Kutta schemes are
applied in the temporal direction. Theoretical analysis indicates that the proposed
schemes conserve mass and preserve the maximum principle under reasonable time
step-size restriction, which is independent of the space step size. Finally, the theoretical
analysis is verified by several numerical examples.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2021-0325},
url = {https://global-sci.com/article/72829/fourth-order-structure-preserving-method-for-the-conservative-allen-cahn-equation}
}