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WENO schemes with Z-type non-linear weighting procedure for fractional differential equations | ||
| Journal of Mathematical Modeling | ||
| مقاله 11، دوره 10، شماره 4، اسفند 2022، صفحه 555-567 اصل مقاله (217.65 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2022.22535.1988 | ||
| نویسنده | ||
| Rooholah Abedian* | ||
| School of Engineering Science, College of Engineering, University of Tehran, Iran | ||
| چکیده | ||
| In this paper, a new fourth-order finite difference weighted essentially non-oscillatory (WENO) scheme is developed for the fractional differential equations which may contain non-smooth solutions at a later time, even if the initial solution is smooth enough. A set of Z-type non-linear weights is constructed based on the $L_1$ norm, yielding improved WENO scheme with more accurate resolution. The Caputo fractional derivative of order $\alpha$ is split into a weakly singular integral and a classical second derivative. The classical Gauss-Jacobi quadrature is employed for solving the weakly singular integral. Also, a new WENO-type reconstruction methodology for approximating the second derivative is developed. Some benchmark examples are prepared to illustrate the efficiency, robustness, and good performance of this new finite difference WENO-Z scheme. | ||
| کلیدواژه‌ها | ||
| Finite difference scheme؛ fractional differential equations؛ WENO-Z scheme | ||
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آمار تعداد مشاهده مقاله: 777 تعداد دریافت فایل اصل مقاله: 348 |
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