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

Xiaohan Cheng, Jianhu Feng (), Supei Zheng () and Xueli Song ()
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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

International Journal of Modern Physics C (IJMPC), 2019, vol. 30, issue 02n03, 1-16

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.

Keywords: Finite difference method; Hamilton–Jacobi equations; WENO reconstruction; nonlinear weights; high-order (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S0129183119500207

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