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 |
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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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| _version_ | 1832558360341250048 |
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| author | Chaeyoung Lee Jintae Park Soobin Kwak Sangkwon Kim Yongho Choi Seokjun Ham Junseok Kim |
| author_facet | Chaeyoung Lee Jintae Park Soobin Kwak Sangkwon Kim Yongho Choi Seokjun Ham Junseok Kim |
| author_sort | Chaeyoung Lee |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0316f381ee4e44a78039067156ff9c33 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-0316f381ee4e44a78039067156ff9c332025-02-03T01:32:28ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/2731593An Adaptive Time-Stepping Algorithm for the Allen–Cahn EquationChaeyoung Lee0Jintae Park1Soobin Kwak2Sangkwon Kim3Yongho Choi4Seokjun Ham5Junseok Kim6Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of Computer & Information Engineering (Information Security)Department of MathematicsDepartment of MathematicsIn 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.http://dx.doi.org/10.1155/2022/2731593 |
| spellingShingle | Chaeyoung Lee Jintae Park Soobin Kwak Sangkwon Kim Yongho Choi Seokjun Ham Junseok Kim An Adaptive Time-Stepping Algorithm for the Allen–Cahn Equation Journal of Function Spaces |
| title | An Adaptive Time-Stepping Algorithm for the Allen–Cahn Equation |
| title_full | An Adaptive Time-Stepping Algorithm for the Allen–Cahn Equation |
| title_fullStr | An Adaptive Time-Stepping Algorithm for the Allen–Cahn Equation |
| title_full_unstemmed | An Adaptive Time-Stepping Algorithm for the Allen–Cahn Equation |
| title_short | An Adaptive Time-Stepping Algorithm for the Allen–Cahn Equation |
| title_sort | adaptive time stepping algorithm for the allen cahn equation |
| url | http://dx.doi.org/10.1155/2022/2731593 |
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