Remarks on Numerical Experiments of the Allen-Cahn Equations with Constraint via Yosida Approximation

We consider a one-dimensional Allen–Cahn equation with constraint from the view-point of numerical analysis. Our constraint is the subdifferential of the indicator function on the closed interval, which is the multivalued function. Therefore, it is very difficult to make numerical experiments of our equation. In this paper we approximate our constraint by Yosida approximation. Then, we study the approximating system of our original model numerically. In particular, we give the criteria for the standard forward Euler method to give stable numerical experiments of our approximating equation. Moreover, we give some numerical experiments of approximating equation.