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Open AccessArticle

Reinterpretation of Multi-Stage Methods for Stiff Systems: A Comprehensive Review on Current Perspectives and Recommendations

by Yonghyeon Jeon 1,†, Soyoon Bak 1,† and Sunyoung Bu 2,*
1
Department of Mathematics, Kyungpook National University, Daegu 41566, Korea
2
Department of Liberal Arts, Hongik university, Sejong 30016, Korea
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2019, 7(12), 1158; https://doi.org/10.3390/math7121158
Received: 9 November 2019 / Revised: 23 November 2019 / Accepted: 26 November 2019 / Published: 1 December 2019
In this paper, we compare a multi-step method and a multi-stage method for stiff initial value problems. Traditionally, the multi-step method has been preferred than the multi-stage for a stiff problem, to avoid an enormous amount of computational costs required to solve a massive linear system provided by the linearization of a highly stiff system. We investigate the possibility of usage of multi-stage methods for stiff systems by discussing the difference between the two methods in several numerical experiments. Moreover, the advantages of multi-stage methods are heuristically presented even for nonlinear stiff systems through several numerical tests. View Full-Text
Keywords: multi-stage method; multi-step method; Runge–Kutta method; backward difference formula; stiff system multi-stage method; multi-step method; Runge–Kutta method; backward difference formula; stiff system
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Jeon, Y.; Bak, S.; Bu, S. Reinterpretation of Multi-Stage Methods for Stiff Systems: A Comprehensive Review on Current Perspectives and Recommendations. Mathematics 2019, 7, 1158.

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