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DOI number:10.1080/00207160.2026.2614072

Journal:International Journal of Computer Mathematics

Abstract:Numerical solutions of Allen–Cahn equation with variable diffusive coefficient are studied. First, we give some analysis to the steady-state Allen–Cahn equation, where by using the shooting method, we find three classical solutions to this nonlinear boundary value problem. This verifies the existence of steady state of time-dependent Allen–Cahn equationwhen time variable approaches to infinity. A standard fully discrete scheme for new Allen–Cahn equation is considered, where the second-order stabilized CNAB approximation in time and a central difference discretization in space are employed. Further, bearing a resemblance to numerical analysis for Allen–Cahn equation with constant coefficients, we prove the numerical scheme satisfies the discrete maximum principle under some mild constraints. Based on the numerical stability, the nonlinear energy stability of the fully discrete scheme is established, and the corresponding error estimate is established. Finally, numerical experiments with particular spacedependent coefficients are carried out which support the theoretical results of our investigation.

Indexed by:Journal paper

Correspondence Author:Zhijian Ye, Puxin Guo, Yufeng Xu*, Zhoushun Zheng

Discipline:Natural Science

First-Level Discipline:Mathematics

Document Type:J

Volume:103

Issue:6

Page Number:1329--1349

Translation or Not:no

Date of Publication:2026-01-13

Included Journals:SCI

Links to published journals:https://www.tandfonline.com/doi/full/10.1080/00207160.2026.2614072

Date of Publication:2026-01-13