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Stability of Newton TVD Runge–Kutta scheme for one-dimensional Euler equations with adaptive mesh

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  • Yuan, Xinpeng
  • Ning, Jianguo
  • Ma, Tianbao
  • Wang, Cheng

Abstract

In this paper, we propose a moving mesh method with a Newton total variation diminishing (TVD) Runge–Kutta scheme for the Euler equations. Our scheme improves time discretization in the moving mesh algorithms. By analyzing the semi-discrete Euler equations with the discrete moving mesh equations as constraints, the stability of the Newton TVD Runge–Kutta scheme is proved. Thus, we can conclude that the proposed algorithm can generate a weak solution to the Euler equations. Finally, numerical examples are presented to verify the theoretical results and demonstrate the accuracy of the proposed scheme.

Suggested Citation

  • Yuan, Xinpeng & Ning, Jianguo & Ma, Tianbao & Wang, Cheng, 2016. "Stability of Newton TVD Runge–Kutta scheme for one-dimensional Euler equations with adaptive mesh," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 1-16.
    • Handle: RePEc:eee:apmaco:v:282:y:2016:i:c:p:1-16
    DOI: 10.1016/j.amc.2016.02.006
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    Cited by:

    1. Porubov, A.V. & Bondarenkov, R.S. & Bouche, D. & Fradkov, A.L., 2018. "Two-step shock waves propagation for isothermal Euler equations," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 160-166.
    2. Yuan, Xinpeng & Wang, Fang & Xue, Yakui & Liu, Maoxing, 2018. "Global stability of an SIR model with differential infectivity on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 443-456.

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