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Hokkaido University Preprint Series in Mathematics >
Remarks on numerical experiments of Allen-Cahnequations with constraint via Yosida approximation
| Title: | Remarks on numerical experiments of Allen-Cahnequations with constraint via Yosida approximation |
| Authors: | Suzuki, Tomoyuki Browse this author | | Takasao, Keisuke Browse this author | | YAMAZAKI, NORIAKI Browse this author |
| Keywords: | Allen{Cahn equation, constraint, subdifferential, Yosida approximation, singular limit, numerical experiments. |
| Issue Date: | 12-Nov-2015 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1079 |
| Start Page: | 1 |
| End Page: | 38 |
| Abstract: | We consider a one-dimensional Allen{Cahn equation with con- straint from the view-point of numerical analysis. Our constraint is the subdifferential of the indicator function on the closed interval, which is the multivalued function. Therefore, it is very difficult to make numerical ex- periments of our equation. In this paper we approximate our constraint by Yosida approximation. Then, we study the approximating system of our original model numerically. In particular, we give the criteria for the stan- dard forward Euler method to give stable numerical experiments of our approximating equation. Moreover, we give some numerical experiments of approximating equation. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69883 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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