Papers - OKUMURA Makoto
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Structure-preserving schemes for Cahn–Hilliard equations with dynamic boundary conditions Reviewed
Makoto Okumura, Takeshi Fukao
Discrete and Continuous Dynamical Systems - S 17 ( 1 ) 362 - 394 2024.1
Authorship：Lead author, Corresponding author Publisher：American Institute of Mathematical Sciences (AIMS)
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Keisuke Imafuku, Hiroaki Iwata, Ken Natsuga, Makoto Okumura, Yasuaki Kobayashi, Hiroyuki Kitahata, Akiharu Kubo, Masaharu Nagayama, Hideyuki Ujiie
Cell Proliferation 56 ( 9 ) e13441 2023.3
Publisher：Wiley
DOI： 10.1111/cpr.13441
Other Link： https://onlinelibrary.wiley.com/doi/full-xml/10.1111/cpr.13441
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A second-order accurate structure-preserving scheme for the Cahn-Hilliard equation with a dynamic boundary condition Reviewed
Makoto Okumura, Takeshi Fukao, Daisuke Furihata, Shuji Yoshikawa
Communications on Pure & Applied Analysis 21 ( 2 ) 355 - 355 2022.2
Authorship：Lead author Publisher：American Institute of Mathematical Sciences (AIMS)
<p lang="fr"><p style='text-indent:20px;'>We propose a structure-preserving finite difference scheme for the Cahn–Hilliard equation with a dynamic boundary condition using the discrete variational derivative method (DVDM) proposed by Furihata and Matsuo [<xref ref-type="bibr" rid="b14">14</xref>]. In this approach, it is important and essential how to discretize the energy which characterizes the equation. By modifying the conventional manner and using an appropriate summation-by-parts formula, we can use a standard central difference operator as an approximation of an outward normal derivative on the discrete boundary condition of the scheme. We show that our proposed scheme is second-order accurate in space, although the previous structure-preserving scheme proposed by Fukao–Yoshikawa–Wada [<xref ref-type="bibr" rid="b13">13</xref>] is first-order accurate in space. Also, we show the stability, the existence, and the uniqueness of the solution for our proposed scheme. Computation examples demonstrate the effectiveness of our proposed scheme. Especially through computation examples, we confirm that numerical solutions can be stably obtained by our proposed scheme.</p></p>
DOI： 10.3934/cpaa.2021181
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A new structure-preserving scheme with the staggered space mesh for the Cahn–Hilliard equation under a dynamic boundary condition Reviewed
Makoto Okumura, Takeshi Fukao
Advances in Mathematical Sciences and Applications 30 ( 2 ) 347 - 376 2021.8
Authorship：Lead author Publisher：Gakkotosho
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Numerical results for ordinary and partial differential equations describing motions of elastic materials Reviewed International coauthorship
Chiharu Kosugi, Toyohiko Aiki, Martijn Anthonissen, Makoto Okumura
Advances in Mathematical Sciences and Applications 30 ( 2 ) 387 - 414 2021.8
Publisher：Gakkotosho
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A structure-preserving scheme for the Allen–Cahn equation with a dynamic boundary condition Reviewed
Makoto Okumura, Daisuke Furihata
Discrete & Continuous Dynamical Systems - A 40 ( 8 ) 4927 - 4960 2020.5
Authorship：Lead author Publisher：American Institute of Mathematical Sciences (AIMS)
DOI： 10.3934/dcds.2020206
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A stable and structure-preserving scheme for a non-local Allen–Cahn equation Reviewed
Makoto Okumura
Japan Journal of Industrial and Applied Mathematics 35 ( 3 ) 1245 - 1281 2018.9
Authorship：Lead author, Corresponding author