A sixth-order finite difference WENO scheme for Hamilton–Jacobi equations

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.

KEYWORDS:

• Finite difference method
• Hamilton–Jacobi equations
• WENO scheme
• high order
• upwind scheme

2010 AMS SUBJECT CLASSIFICATIONS:

• 65M06
• 70H20

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.

Additional information

Funding

This research is supported by the National Natural Science Foundation of China (Grant no. 11601037 and 11401045) and the Special Fund for Basic Scientific Research of Central Universities in Chang'an University (Grant no. 310812171002).