Abstract
In this paper, we propose a new linear second-order finite difference scheme for Allen–Cahn equations. We use a modified Leap-Frog finite difference scheme with stabilized term and a central finite difference scheme for temporal and spatial discretization respectively. It is shown that the discrete maximum principle holds under reasonable constraints on time step size and coefficient of stabilized term. Based on the maximum stability, the maximum-norm error is analyzed. Moreover, we can see that the proposed scheme is unconditionally energy-stable. Finally, a numerical experiment is performed to verify the theoretical results.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.