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

Yonghyeon Jeon, Soyoon Bak and Sunyoung Bu
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Yonghyeon Jeon: Department of Mathematics, Kyungpook National University, Daegu 41566, Korea
Soyoon Bak: Department of Mathematics, Kyungpook National University, Daegu 41566, Korea
Sunyoung Bu: Department of Liberal Arts, Hongik university, Sejong 30016, Korea

Mathematics, 2019, vol. 7, issue 12, 1-14

Abstract: 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.

Keywords: multi-stage method; multi-step method; Runge–Kutta method; backward difference formula; stiff system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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