An adaptive time-step method for a nonlocal version of the Allen-Cahn equation
Ana-Maria Moşneagu, Iulian Stoleriu · Discrete and Continuous Dynamical Systems - S · 2024
In this paper, we propose an efficient numerical method with adaptive time-step size for a nonlocal version of the Allen-Cahn equation. The nonlocal model was introduced as an alternative model for phase transitions in solids. This model becomes very useful when the transition process operates at very small length scales, case in which its local correspondent could not be applied. Our numerical approach is based on Runge-Kutta-Fehlberg technique and also on a predictor-corrector method. Some computational experiments are made to illustrate the effectiveness of the proposed method, with the goal of saving the calculation costs and also of capturing the different time scales that arise in the evolution of the solution.