Stability and Robustness of Time-discretization Schemes for the
Allen-Cahn Equation via Bifurcation and Perturbation Analysis
Stability and Robustness of Time-discretization Schemes for the
Allen-Cahn Equation via Bifurcation and Perturbation Analysis
The Allen-Cahn equation is a fundamental model for phase transitions, offering critical insights into the dynamics of interface evolution in various physical systems. This paper investigates the stability and robustness of frequently utilized time-discretization numerical schemes for solving the Allen-Cahn equation, with focuses on the Backward Euler, Crank-Nicolson (CN), convex …