Stability and convergence of Strang splitting. Part I: Scalar Allen-Cahn equation

We consider a class of second-order Strang splitting methods for Allen-Cahn equations with polynomial or logarithmic nonlinearities. For the case both linear and nonlinear propagators are computed explicitly. show that this type scheme is unconditionally stable regardless time step. Moreover we establish strict energy dissipation judiciously modified which coincides classical up to $\mathcal O(\tau)$ where $\tau$ potential case, since continuous-time propagator no longer enjoys explicit analytic treatments, employ second order in two-stage implicit Runge--Kutta (RK) together an efficient Newton iterative solver. prove maximum principle ensures phase separation law under mild restrictions on These appear be first rigorous results Strang-type equations.