An embedded formula of the Chebyshev collocation method for stiff problems
- Authors
- Piao, Xiangfan; Bu, Sunyoung; Kim, Dojin; Kim, Philsu
- Issue Date
- 15-Dec-2017
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Generalized Chebyshev polynomial; Collocation method; Embedded formula; Stiff initial value problem
- Citation
- JOURNAL OF COMPUTATIONAL PHYSICS, v.351, pp.376 - 391
- Journal Title
- JOURNAL OF COMPUTATIONAL PHYSICS
- Volume
- 351
- Start Page
- 376
- End Page
- 391
- URI
- https://scholarworks.bwise.kr/hongik/handle/2020.sw.hongik/4889
- DOI
- 10.1016/j.jcp.2017.09.046
- ISSN
- 0021-9991
- Abstract
- In this study, we have developed an embedded formula of the Chebyshev collocation method for stiff problems, based on the zeros of the generalized Chebyshev polynomials. A new strategy for the embedded formula, using a pair of methods to estimate the local truncation error, as performed in traditional embedded Runge-Kutta schemes, is proposed. The method is performed in such a way that not only the stability region of the embedded formula can be widened, but by allowing the usage of larger time step sizes, the total computational costs can also be reduced. In terms of concrete convergence and stability analysis, the constructed algorithm turns out to have an 8th order convergence and it exhibits A-stability. Through several numerical experimental results, we have demonstrated that the proposed method is numerically more efficient, compared to several existing implicit methods. (C) 2017 Elsevier Inc. All rights reserved.
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Collections - College of Science and Technology > Department of Computer and Information Communications Engineering > 1. Journal Articles
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