RT - Journal Article T1 - WENO-Z Schemes with Legendre Basis for non-Linear Degenerate Parabolic Equations JF - IJMSI YR - 2021 JO - IJMSI VO - 16 IS - 2 UR - http://ijmsi.ir/article-1-1292-en.html SP - 125 EP - 143 K1 - WENO schemes K1 - Legendre orthogonal polynomials K1 - multidimensional non-linear degenerate parabolic equations K1 - porous medium equation. AB - This paper provides a fourth-order scheme for approximating solutions of non-linear degenerate parabolic equations that their solutions may contain discontinuity. In the reconstruction step, a fourth-order weighted essentially non-oscillatory (WENO) reconstruction in Legendre basis, written as a convex combination of interpolants based on different stencils, is constructed. In the one-dimensional case, the new fourth-order reconstruction is based on a four-point stencil. The most important subject is that one of these interpolation polynomials is taken as a quadratic polynomial, and the linear weights of the symmetric and convex combination are set as to get fourth-order accuracy in smooth areas. Following the methodology of the traditional WENO-Z reconstruction, the non-oscillatory weights is calculated by the linear weights. The accuracy, robustness, and high-resolution properties of the new procedure are shown by extensive numerical examples. LA eng UL http://ijmsi.ir/article-1-1292-en.html M3 10.52547/ijmsi.16.2.125 ER -