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WENO scheme with new smoothness indicator for Hamilton–Jacobi equation

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  • Huang, Cong

Abstract

In this paper, we develop a new weighted essentially non-oscillatory (WENO) scheme for Hamilton–Jacobi (HJ) equation by proposing a new family of smoothness indicators, which includes the smoothness indicator in Jiang and Peng (2000) as one of its members. The new family of smoothness indicators has three parameters. By choosing the parameters properly, the new WENO scheme provides more accurate numerical solution than the original one, and increases little computational cost.

Suggested Citation

  • Huang, Cong, 2016. "WENO scheme with new smoothness indicator for Hamilton–Jacobi equation," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 21-32.
    • Handle: RePEc:eee:apmaco:v:290:y:2016:i:c:p:21-32
    DOI: 10.1016/j.amc.2016.05.022
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    References listed on IDEAS

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    1. Feng, Hui & Huang, Cong & Wang, Rong, 2014. "An improved mapped weighted essentially non-oscillatory scheme," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 453-468.
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    Cited by:

    1. Hajipour, Mojtaba & Jajarmi, Amin & Malek, Alaeddin & Baleanu, Dumitru, 2018. "Positivity-preserving sixth-order implicit finite difference weighted essentially non-oscillatory scheme for the nonlinear heat equation," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 146-158.
    2. Omer Musa & Guoping Huang & Mingsheng Wang, 2020. "A New Smoothness Indicator of Adaptive Order Weighted Essentially Non-Oscillatory Scheme for Hyperbolic Conservation Laws," Mathematics, MDPI, vol. 9(1), pages 1-31, December.

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