weno-z schemes based on the identification of extreme points for degenerate parabolic equations

Here, based on the specified format, the abstract is discussed.✓ motivation or purpose: the degenerate parabolic equation appears in a wide range ofapplications such as porous medium equation.✓ problem: in general, this equation does not have a classical solution even if it has a smoothinitial condition, and for this reason, weak solutions have been considered by researchers.✓ method: this equation is solved by a new modified sixth-order finite difference weno-z(mweno-z) reconstruction.✓ results: the mweno-z scheme uses less cpu times to reach certain error levels thanthat for the classical weno scheme for degenerate parabolic equations.✓ conclusions: comparing mweno-z with the classical weno, the new mweno-zscheme is more efficient and robust by using a normal cfl number without any furtherpositivity preserving procedure.