The ETDRKP-IF scheme for Allen-Cahn equation with logarithmic Flory-Huggins potential

Abstract

Thispaperfocusesoncombiningthefourth-order central difference schemewith the fourth-order exponential time-differencingRunge-Kutta (ETDRK4P)methodbasedon Pad´erationalapproximationofmatrixexponential,alongwith dimensional splitting. The resulting ETDRKP-IF scheme is applied to solve the Allen-Cahn equationwith logarithmic Flory-Hugginspotential.Theproposedmethodachievesfourth orderaccuracyinbothtimeandspace.Numericalexperiments verify the convergence and energy stability of the scheme, providing a reliablemethod for numerical simulationof the Allen-CahnequationwithlogarithmicFlory-Hugginspotential.