In this research, a class of radial basis functions (RBFs) ENO/WENO schemes with a Lax–Wendroff time discretization procedure, named as RENO/RWENO‐LW, for solving Hamilton–Jacobi (H–J) equations is designed. Particularly the multi‐quadratic RBFs are used. These schemes enhance the local accuracy and convergence by locally optimizing the shape parameters. Comparing with the original WENO with Lax–Wendroff time discretization schemes of Qiu for HJ equations, the new schemes provide more accurate reconstructions and sharper solution profiles near strong discontinuous derivative. Also, the RENO/RWENO‐LW schemes are easy to implement in the existing original ENO/WENO code. Extensive numerical experiments are considered to verify the capability of the new schemes.

中文翻译：

---

带有Lax-Wendroff类型时间离散化的RBF-ENO / WENO方案，用于Hamilton-Jacobi方程

在这项研究中，设计了一类具有Lax–Wendroff时间离散化过程的径向基函数（NOF）ENO / WENO方案，称为RENO / RWENO–LW，用于求解Hamilton–Jacobi（H–J）方程。特别是使用多二次RBF。这些方案通过局部优化形状参数来提高局部精度和收敛性。与原始的WENO和针对HJ方程的Qiu的Lax–Wendroff时间离散化方案相比，新方案在强不连续导数附近提供了更准确的重构和更清晰的解轮廓。同样，RENO / RWENO-LW方案很容易在现有的原始ENO / WENO代码中实现。考虑了广泛的数值实验，以验证新方案的能力。