Abstract
This article aims to solve the nonlinear Allen-Cahn equation numerically. The diagonally implicit fractional-step theta-(DIFST) scheme is used for the discretization of the time derivative term while the space derivative is discretized by the conforming finite element method. The computational efficiency of the DIFST scheme in terms of CPU time and temporal error estimation is computed and compared with other time discretization schemes. Several test problems are presented to show the effectiveness of the DIFST scheme.