  In this paper, a class of high order numerical schemes is proposed for
solving Hamilton-Jacobi (H-J) equations. This work is regarded as an extension
of our previous work for nonlinear degenerate parabolic equations, see
Christlieb et al. \emph{arXiv preprint arXiv:1707.09294},, which relies on a
special kernel-based formulation of the solutions and successive convolution.
When applied to the H-J equations, the newly proposed scheme attains genuinely
high order accuracy in both space and time, and more importantly, it is
unconditionally stable, hence allowing for much larger time step evolution
compared with other explicit schemes and saving computational cost. A high
order weighted essentially non-oscillatory methodology and a novel nonlinear
filter are further incorporated to capture the correct viscosity solution.
Furthermore, by coupling the recently proposed inverse Lax-Wendroff boundary
treatment technique, this method is very flexible in handing complex geometry
as well as general boundary conditions. We perform numerical experiments on a
collection of numerical examples, including H-J equations with linear,
nonlinear, convex or non-convex Hamiltonians. The efficacy and efficiency of
the proposed scheme in approximating the viscosity solution of general H-J
equations is verified.
