A sixth-order central WENO scheme for nonlinear degenerate parabolic equations

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