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A new type of finite difference WENO schemes for Hamilton–Jacobi equations

Author

Listed:
  • Xiaohan Cheng

    (School of Science, Chang’an University, Xi’an 710064, P. R. China)

  • Jianhu Feng

    (School of Science, Chang’an University, Xi’an 710064, P. R. China)

  • Supei Zheng

    (School of Science, Chang’an University, Xi’an 710064, P. R. China)

  • Xueli Song

    (School of Science, Chang’an University, Xi’an 710064, P. R. China)

Abstract

In this paper, we propose a new type of finite difference weighted essentially nonoscillatory (WENO) schemes to approximate the viscosity solutions of the Hamilton–Jacobi equations. The new scheme has three properties: (1) the scheme is fifth-order accurate in smooth regions while keep sharp discontinuous transitions with no spurious oscillations near discontinuities; (2) the linear weights can be any positive numbers with the symmetry requirement and that their sum equals one; (3) the scheme can avoid the clipping of extrema. Extensive numerical examples are provided to demonstrate the accuracy and the robustness of the proposed scheme.

Suggested Citation

  • Xiaohan Cheng & Jianhu Feng & Supei Zheng & Xueli Song, 2019. "A new type of finite difference WENO schemes for Hamilton–Jacobi equations," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 30(02n03), pages 1-16, February.
    • Handle: RePEc:wsi:ijmpcx:v:30:y:2019:i:02n03:n:s0129183119500207
    DOI: 10.1142/S0129183119500207
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