Volume 16, Issue 2 (10-2021)                   IJMSI 2021, 16(2): 125-143 | Back to browse issues page

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Abedian R. WENO-Z Schemes with Legendre Basis for non-Linear Degenerate Parabolic Equations. IJMSI 2021; 16 (2) :125-143
URL: http://ijmsi.ir/article-1-1292-en.html

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.

Type of Study: Research paper | Subject: Special

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