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A unified Explicit form for difference formulas for fractional and classical derivatives and applications | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 03 اردیبهشت 1403 اصل مقاله (677.86 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2023.58229.2459 | ||
| نویسندگان | ||
| W. Anura Gunarathna1؛ Haniffa Mohamed Nasir* 2؛ Wasantha B. Daundasekera3 | ||
| 1Department of Physical Sciences, College of Applied Sciences, Rajarata University, Sri Lanka. | ||
| 2FracDiff Research Group, Department of Mathematics, P. O. Box: 36, Sultan Qaboos University, Al-Khoud 123, Muscat, Sultanate of Oman. | ||
| 3Department of Mathematics, University of Peradeniya, Peradeniya, Sri Lanka. | ||
| چکیده | ||
| A unified explicit form for difference formulas to approximate the fractional and classical derivatives is presented. The formula gives finite difference approximations for any classical derivative with a desired order of accuracy at any nodal point in the computational domain. It also gives Gr\"unwald type approximations for fractional derivatives with arbitrary order of approximation at any point. Thus, this explicit unifies approximations of both types of derivatives. Moreover, for classical derivatives, it provides various finite difference formulas such as forward, backward, central, staggered, compact, non-compact, etc. Efficient computations of the coefficients of the difference formulas are also presented that lead to automating the solution process of differential equations with a given higher order accuracy. Some basic applications are presented to demonstrate the usefulness of this unified formulation. | ||
| کلیدواژه‌ها | ||
| Fractional derivative؛ Shifted Gr"unwald approximation؛ Lubich Generators؛ Compact finite difference formula؛ Boundary value problem | ||
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آمار تعداد مشاهده مقاله: 91 تعداد دریافت فایل اصل مقاله: 55 |
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