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Information Journal Paper

Title

WENO SCHEMES FOR MULTIDIMENSIONAL NONLINEAR DEGENERATE PARABOLIC PDES

Pages

  41-61

Abstract

 In this paper, a scheme is presented for approximating solutions of non-linear degenerate parabolic equations which may contain discontinuous solutions. In the one-dimensional case, following the idea of the local discontinuous Galerkin method, first the degenerate parabolic equation is considered asa nonlinear system of first order equations, and then this system is solved using a fifth-order finite difference weighted essentially nonoscillatory (WENO) method for conservation laws. This is the first time that the minmod-limiter combined with weighted essentially nonoscillatory procedure has been applied to the degenerate parabolic equations. Also, it is necessary to mention that the new scheme has fifth-order accuracy in smooth regions and second-order accuracy near singularities. The accuracy, robustness, and high-resolution properties of the new scheme are demonstrated in a variety of multidimen- sional problems.

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    • Cite

    APA: Copy

    ABEDIAN, R.. (2018). WENO SCHEMES FOR MULTIDIMENSIONAL NONLINEAR DEGENERATE PARABOLIC PDES. IRANIAN JOURNAL OF NUMERICAL ANALYSIS AND OPTIMIZATION, 8(1 (SERIAL NUMBER 13) ), 41-61. SID. https://sid.ir/paper/260841/en

    Vancouver: Copy

    ABEDIAN R.. WENO SCHEMES FOR MULTIDIMENSIONAL NONLINEAR DEGENERATE PARABOLIC PDES. IRANIAN JOURNAL OF NUMERICAL ANALYSIS AND OPTIMIZATION[Internet]. 2018;8(1 (SERIAL NUMBER 13) ):41-61. Available from: https://sid.ir/paper/260841/en

    IEEE: Copy

    R. ABEDIAN, “WENO SCHEMES FOR MULTIDIMENSIONAL NONLINEAR DEGENERATE PARABOLIC PDES,” IRANIAN JOURNAL OF NUMERICAL ANALYSIS AND OPTIMIZATION, vol. 8, no. 1 (SERIAL NUMBER 13) , pp. 41–61, 2018, [Online]. Available: https://sid.ir/paper/260841/en

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