A maximum-principle preserving and unconditionally energy-stable linear second-order finite difference scheme for Allen-Cahn equations. (English) Zbl 1524.65336
Summary: In this paper, we propose a new linear second-order finite difference scheme for Allen-Cahn equations. We use a modified Leap-Frog finite difference scheme with stabilized term and a central finite difference scheme for temporal and spatial discretization respectively. It is shown that the discrete maximum principle holds under reasonable constraints on time step size and coefficient of stabilized term. Based on the maximum stability, the maximum-norm error is analyzed. Moreover, we can see that the proposed scheme is unconditionally energy-stable. Finally, a numerical experiment is performed to verify the theoretical results.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
Keywords:
Allen-Cahn equation; leap-frog scheme; finite difference method; discrete maximum principle; discrete energy stabilityReferences:
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