Explicit, linear, energy stable, and maximum principle preserving method for Allen-Cahn equation

초록

We propose an explicit linear scheme for the Allen-Cahn equation that satisfies both energy stability and the maximum principle. This approach is based on a finite-difference spatial discretization; additionally, energy stability and maximum principle are proved without time-step restrictions. The proposed method can be easily extended to second-order accuracy in time. Numerical experiments demonstrate the accuracy, efficiency, energy stability, and maximum principle of the proposed scheme.

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