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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 | ||
آمار تعداد مشاهده مقاله: 774 تعداد دریافت فایل اصل مقاله: 345 |