An Adaptive Time-Stepping Algorithm for the Allen–Cahn Equation
In this paper, we present a simple and accurate adaptive time-stepping algorithm for the Allen–Cahn (AC) equation. The AC equation is a nonlinear partial differential equation, which was first proposed by Allen and Cahn for antiphase boundary motion and antiphase domain coarsening. The mathematical...
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| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/2731593 |
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| Summary: | In this paper, we present a simple and accurate adaptive time-stepping algorithm for the Allen–Cahn (AC) equation. The AC equation is a nonlinear partial differential equation, which was first proposed by Allen and Cahn for antiphase boundary motion and antiphase domain coarsening. The mathematical equation is a building block for modelling many interesting interfacial phenomena such as dendritic crystal growth, multiphase fluid flows, and motion by mean curvature. The proposed adaptive time-stepping algorithm is based on the Runge–Kutta–Fehlberg method, where the local truncation error is estimated by using fourth- and fifth-order numerical schemes. Computational experiments demonstrate that the proposed time-stepping technique is efficient in multiscale computations, i.e., both the fast and slow dynamics. |
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| ISSN: | 2314-8888 |