Collocation-based numerical simulation of fractional order Allen–Cahn equation.

This article looks for a reliable numerical technique to solve the Allen–Cahn equation using the Caputo time-fractional derivative. The fractional derivative semi-discretization approach using finite differences of the second order is shown first. The cubic B-spline collocation method is used to get a full discretization. We prove the conditional stability and convergence of the suggested approach. The technique's effectiveness is demonstrated with numerical examples using two test problems. Numerical analysis confirms the approach's efficiency and the method's continued correctness. [ABSTRACT FROM AUTHOR]