Iranian Journal of Mathematical Sciences and Informatics
مجله علوم ریاضی و انفورماتیک
IJMSI
Basic Sciences
http://ijmsi.ir
1
admin
1735-4463
2008-9473
8
10.61186/ijmsi
14
8888
13
en
jalali
1400
7
1
gregorian
2021
10
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16
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online
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fulltext
en
WENO-Z Schemes with Legendre Basis for non-Linear Degenerate Parabolic Equations
تخصصي
Special
پژوهشي
Research paper
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<p style="margin: 0px; text-align: justify;">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 <span style="text-align: justify;">are shown by extensive numerical examples.</span></p>
WENO schemes, Legendre orthogonal polynomials, multidimensional non-linear degenerate parabolic equations, porous medium equation.
125
143
http://ijmsi.ir/browse.php?a_code=A-10-3361-1&slc_lang=en&sid=1
R.
Abedian
rabedian@ut.ac.ir
10031947532846008810
10031947532846008810
Yes
University of Tehran