Abstract
Purpose - The purpose of this paper is to present some numerical methods based on different time stepping and space discretization methods for the Allen-Cahn equation with non-periodic boundary conditions.
Design/methodology/approach - In space the equation is discretized by the Chebyshev spectral method, while in time the exponential time differencing fourth-order Runge-Kutta (ETDRK4) and implicit-explicit scheme are used. Also, for comparison the finite difference scheme in both space and time is used.
Findings - It is found that the use of implicit-explicit scheme allows use of a large time-step, since an explicit method has less order of accuracy as compared to implicit-explicit method. In time-stepping the proposed ETDRK4 does not behave well for this special kind of partial differential equation.
Originality/value - The paper presents some numerical methods based on different time stepping and space discretization methods for the Allen-Cahn equation with non-periodic boundary conditions.