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자연과학대학
수학전공
Journal papers
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An energy stable Runge–Kutta method for convex gradient problems
Title
An energy stable Runge–Kutta method for convex gradient problems
Authors
Shin J.
;
Lee J.-Y.
Ewha Authors
이준엽
;
신재민
SCOPUS Author ID
이준엽
; 신재민
Issue Date
2020
Journal Title
Journal of Computational and Applied Mathematics
ISSN
0377-0427
Citation
Journal of Computational and Applied Mathematics vol. 367
Keywords
Convex problem
;
Gradient flow
;
Positive definite condition
;
Stiffly accurate Runge–Kutta method
;
Unconditional energy stability
;
Unique solvability
Publisher
Elsevier B.V.
Indexed
SCIE; SCOPUS
Document Type
Article
Abstract
We propose a class of Runge–Kutta methods which provide a simple unified framework to solve the gradient flow of a convex functional in an unconditionally energy stable manner. Stiffly accurate Runge–Kutta methods are high order accurate in terms of time and also assure the energy stability for any time step size when they satisfy the positive definite condition. We provide a detailed proof of the unconditional energy stability as well as unique solvability of the proposed scheme. We demonstrate the accuracy and stability of the proposed methods using numerical experiments for a specific example. © 2019 Elsevier B.V.
DOI
10.1016/j.cam.2019.112455
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