Next Article in Journal
Efficient Pipelined Broadcast with Monitoring Processing Node Status on a Multi-Core Processor
Next Article in Special Issue
Numerical Solutions for Multi-Term Fractional Order Differential Equations with Fractional Taylor Operational Matrix of Fractional Integration
Previous Article in Journal
Analysis and Nonstandard Numerical Design of a Discrete Three-Dimensional Hepatitis B Epidemic Model
Previous Article in Special Issue
Second Order Semilinear Volterra-Type Integro-Differential Equations with Non-Instantaneous Impulses
Open AccessArticle

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

by 1,†, 1,† and 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
Show Figures

Figure 1

MDPI and ACS Style

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. https://doi.org/10.3390/math7121158

AMA Style

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(12):1158. https://doi.org/10.3390/math7121158

Chicago/Turabian Style

Jeon, Yonghyeon; Bak, Soyoon; Bu, Sunyoung. 2019. "Reinterpretation of Multi-Stage Methods for Stiff Systems: A Comprehensive Review on Current Perspectives and Recommendations" Mathematics 7, no. 12: 1158. https://doi.org/10.3390/math7121158

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop