ABSTRACT
In this paper, a sixth-order finite difference weighted essentially non-oscillatory (WENO) scheme is developed to approximate the viscosity solution of the Hamilton–Jacobi equations. This new WENO scheme has the same spatial nodes as the classical fifth-order WENO scheme proposed by Jiang and Peng [Weighted ENO schemes for Hamilton–Jacobi equations, SIAM. J. Sci. Comput. 21 (2000), pp. 2126–2143] but can be as high as sixth-order accurate in smooth region while keeping sharp discontinuous transitions with no spurious oscillations near discontinuities. Extensive numerical experiments in one- and two-dimensional cases are carried out to illustrate the capability of the proposed scheme.
Acknowledgements
The authors are very thankful to the reviewers for their invaluable comments and suggestions.
Disclosure statement
No potential conflict of interest was reported by the authors.