  In this paper we develop a new sixth-order finite difference central weighted
essentially non-oscillatory (WENO) scheme with Z-type nonlinear weights for
nonlinear degenerate parabolic equations. The centered polynomial is introduced
for the WENO reconstruction in order to avoid the negative linear weights. We
choose the Z-type nonlinear weights based on the $L^2$-norm smoothness
indicators, yielding the new WENO scheme with more accurate resolution. It is
also confirmed that the proposed central WENO scheme with the devised nonlinear
weights achieves sixth order accuracy in smooth regions. One- and
two-dimensional numerical examples are presented to demonstrate the improved
performance of the proposed central WENO scheme.
