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

Author

Listed:
  • Xueyu Qin

    (National Key Laboratory of Computational Fluid Dynamics, Beihang University, Beijing 100191, China
    School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China)

  • Zhenhua Jiang

    (National Key Laboratory of Computational Fluid Dynamics, Beihang University, Beijing 100191, China
    School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China)

  • Chao Yan

    (National Key Laboratory of Computational Fluid Dynamics, Beihang University, Beijing 100191, China
    School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China)

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.

Suggested Citation

  • Xueyu Qin & Zhenhua Jiang & Chao Yan, 2024. "Strong Stability Preserving Two-Derivative Two-Step Runge-Kutta Methods," Mathematics, MDPI, vol. 12(16), pages 1-23, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2465-:d:1453430
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