In this paper, we propose to combine a new fifth order finite difference weighted essentially non-oscillatory (WENO) scheme with high order fast sweeping methods, for directly solving static Hamilton–Jacobi equations. This is motivated by the work in Xiong et al. (J Sci Comput 45(1–3):514–536, 2010), where a fifth order fast sweeping method base on the classical finite difference WENO scheme is developed. Numerical results in Xiong et al. (2010) show that the iterative numbers of the scheme for some cases are very sensitive to the parameter \(\epsilon \), which is used to avoid the denominator to be 0 in the nonlinear weights. Here we propose to use the new fifth order finite difference WENO-ZQ scheme, which was recently developed in Zhu and Qiu (J Comput Phys 318:110–121, 2016), to alleviate this problem. Besides, to save computational cost from WENO reconstructions, a hybrid finite difference linear and WENO scheme is used, which works more robustly. Numerical experiments will be performed to demonstrate the good performance of the new proposed approach.

在本文中，我们建议将新的五阶有限差分加权基本非振荡（WENO）方案与高阶快速扫描方法结合起来，以直接求解静态Hamilton-Jacobi方程。这是由Xiong等人的工作激发的。（J Sci Comput 45（1-3）：514-536，2010年），其中开发了一种基于经典有限差分WENO方案的五阶快速扫描方法。熊等人的数值结果。（2010年）表明，在某些情况下，该方案的迭代数对参数\（\ epsilon \）非常敏感，用于避免非线性权重中的分母为0。在这里，我们建议使用新的五阶有限差分WENO-ZQ方案来缓解这个问题，该方案最近在Zhu和Qiu（J Comput Phys 318：110–121，2016）中开发。此外，为了节省WENO重构的计算成本，使用了混合有限差分线性和WENO方案，该方案工作更稳定。将进行数值实验，以证明新提出的方法的良好性能。