RBF-ENO/WENOschemes withLax-Wendrofftype time discretizations forHamilton-Jacobiequations

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.