Strong Stability Preserving Two-Derivative Two-Step Runge-Kutta Methods

Xueyu Qin, Zhenhua Jiang () and Chao Yan
Additional contact information
Xueyu Qin: National Key Laboratory of Computational Fluid Dynamics, Beihang University, Beijing 100191, China
Zhenhua Jiang: National Key Laboratory of Computational Fluid Dynamics, Beihang University, Beijing 100191, China
Chao Yan: National Key Laboratory of Computational Fluid Dynamics, Beihang University, Beijing 100191, China

Mathematics, 2024, vol. 12, issue 16, 1-23

Abstract: In this study, we introduce the explicit strong stability preserving (SSP) two-derivative two-step Runge-Kutta (TDTSRK) methods. We propose the order conditions using Albrecht’s approach, comparing to the order conditions expressed in terms of rooted trees, these conditions present a more straightforward form with fewer equations. Furthermore, we develop the SSP theory for the TDTSRK methods under certain assumptions and identify its optimal parameters. We also conduct a comparative analysis of the SSP coefficient among TDTSRK methods, two-derivative Runge-Kutta (TDRK) methods, and Runge-Kutta (RK) methods, both theoretically and numerically. The comparison reveals that the TDTSRK methods in the same order of accuracy have the most effective SSP coefficient. Numerical results demonstrate that the TDTSRK methods are highly efficient in solving the partial differential equation, and the TDTSRK methods can achieve the expected order of accuracy.

Keywords: strong stability preserving; two-step Runge-Kutta methods; multiderivative methods; order conditions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/16/2465/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/16/2465/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:16:p:2465-:d:1453430

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().