  In this paper, a high-order moment-based multi-resolution Hermite weighted
essentially non-oscillatory (HWENO) scheme is designed for hyperbolic
conservation laws. The main idea of this scheme is derived from our previous
work [J. Comput. Phys., 446 (2021) 110653], in which the integral averages of
the function and its first order derivative are used to reconstruct both the
function and its first order derivative values at the boundaries. However, in
this paper, only the function values at the Gauss-Lobatto points in the one or
two dimensional case need to be reconstructed by using the information of the
zeroth and first order moments. In addition, an extra modification procedure is
used to modify those first order moments in the troubled-cells, which leads to
an improvement of stability and an enhancement of resolution near
discontinuities. To obtain the same order of accuracy, the size of the stencil
required by this moment-based multi-resolution HWENO scheme is still the same
as the general HWENO scheme and is more compact than the general WENO scheme.
Moreover, the linear weights can also be any positive numbers as long as their
sum equals one and the CFL number can still be 0.6 whether for the one or two
dimensional case. Extensive numerical examples are given to demonstrate the
stability and resolution of such moment-based multi-resolution HWENO scheme.
