A-stable spectral deferred correction method for nonlinear Allen-Cahn model

This paper presents a type of A -stable spectral deferred correction (SDC) method. The scheme is initiated by the first -order backward Euler method. We adopt the linear stabilization approach for the Allen -Cahn model to get the linear semi -implicit SDC scheme. This is done by the addition and subtraction of the linear stabilization operators that have been provided for the Allen -Cahn problem. The ranges of the stabilization factors are then given. The aim is to achieve A -stability and error estimates for the implicit part of the scheme. Finally, the semiimplicit SDC scheme coupled with the Fourier spectral method is used to simulate the Allen -Cahn problem, which is also suitable for the highly nonlinear problem. Numerical experiments are given to numerically demonstrate the high -order accuracy and the energy decay property of the scheme with A -stability parameters.