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Research Articles

Quasi-compact fourth-order approximations for fractional derivatives and applications

Authors:

W. A. Gunarathna ,

Rajarata University of Sri Lanka, LK
About W. A.

Department of Physical Sciences, Faculty of Applied Science

 

Postgraduate Institute of Science, University of Peradeniya, Peradeniya

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H. M. Nasir,

Sultan Qaboos University, OM
About H. M.
FracDiff Research Group, Department of Mathematics, College of Science
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W. B. Daundasekara

University of Peradeniya, Peradeniya, LK
About W. B.
Department of Mathematics, Faculty of Science
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Abstract

Two fourth-order approximations for fractional derivatives are presented. These approximations are constructed from an approximation of order 2 through convex combinations of two different shifts eliminating the third-order term and then approximating the remaining second-order term with a central difference approximation. The constructed approximations are applied in Crank- Nicolson schemes to the one-dimensional space fractional diffusion equation. Numerical tests confirm that the schemes are unconditionally stable for any choice of space discretization and converge with order 4.

How to Cite: Gunarathna, W. A., Nasir, H. M., & Daundasekara, W. B. (2022). Quasi-compact fourth-order approximations for fractional derivatives and applications. Ceylon Journal of Science, 51(5), 589–595. DOI: http://doi.org/10.4038/cjs.v51i5.8085
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Published on 31 Dec 2022.
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