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Gunarathna, Wickramaarachchilage, Nasir, Haniffa Mohamed, Daundasekera, Wasantha. (1403). A unified Explicit form for difference formulas for fractional and classical derivatives and applications. سامانه مدیریت نشریات علمی, 13(1), 307-326. doi: 10.22034/cmde.2023.58229.2459
Wickramaarachchilage Anura Gunarathna; Haniffa Mohamed Nasir; Wasantha Bandara Daundasekera. "A unified Explicit form for difference formulas for fractional and classical derivatives and applications". سامانه مدیریت نشریات علمی, 13, 1, 1403, 307-326. doi: 10.22034/cmde.2023.58229.2459
Gunarathna, Wickramaarachchilage, Nasir, Haniffa Mohamed, Daundasekera, Wasantha. (1403). 'A unified Explicit form for difference formulas for fractional and classical derivatives and applications', سامانه مدیریت نشریات علمی, 13(1), pp. 307-326. doi: 10.22034/cmde.2023.58229.2459
Gunarathna, Wickramaarachchilage, Nasir, Haniffa Mohamed, Daundasekera, Wasantha. A unified Explicit form for difference formulas for fractional and classical derivatives and applications. سامانه مدیریت نشریات علمی, 1403; 13(1): 307-326. doi: 10.22034/cmde.2023.58229.2459

A unified Explicit form for difference formulas for fractional and classical derivatives and applications

Computational Methods for Differential Equations
مقاله 23، دوره 13، شماره 1، فروردین 2025، صفحه 307-326    اصل مقاله (471.29 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.58229.2459
نویسندگان
Wickramaarachchilage Anura Gunarathna1؛ Haniffa Mohamed Nasir* 2؛ Wasantha Bandara 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 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 computational domain. It also gives Gr¨unwald type approximations for fractional derivatives with arbitrary order of approximation at any nodal point. Thus, this explicit form unifies approximations of both types of derivatives. Moreover, for classical derivatives, it also 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 leading 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 Grünwald approximation؛ Lubich Generators؛ Compact finite difference formula؛ Boundary value problem
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