A New Grünwald-Letnikov Derivative Derived from a Second-Order Scheme

B. A. Jacobs

doi:10.1155/2015/952057

A New Grünwald-Letnikov Derivative Derived from a Second-Order Scheme

B. A. Jacobs

University of the Witwatersrand

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

Abstract

A novel derivation of a second-order accurate Grünwald-Letnikov-type approximation to the fractional derivative of a function is presented. This scheme is shown to be second-order accurate under certain modifications to account for poor accuracy in approximating the asymptotic behavior near the lower limit of differentiation. Some example functions are chosen and numerical results are presented to illustrate the efficacy of this new method over some other popular choices for discretizing fractional derivatives.

Original language	English
Article number	952057
Journal	Abstract and Applied Analysis
Volume	2015
DOIs	https://doi.org/10.1155/2015/952057
Publication status	Published - 2015
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

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abstract = "A novel derivation of a second-order accurate Gr{\"u}nwald-Letnikov-type approximation to the fractional derivative of a function is presented. This scheme is shown to be second-order accurate under certain modifications to account for poor accuracy in approximating the asymptotic behavior near the lower limit of differentiation. Some example functions are chosen and numerical results are presented to illustrate the efficacy of this new method over some other popular choices for discretizing fractional derivatives.",

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AB - A novel derivation of a second-order accurate Grünwald-Letnikov-type approximation to the fractional derivative of a function is presented. This scheme is shown to be second-order accurate under certain modifications to account for poor accuracy in approximating the asymptotic behavior near the lower limit of differentiation. Some example functions are chosen and numerical results are presented to illustrate the efficacy of this new method over some other popular choices for discretizing fractional derivatives.

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JO - Abstract and Applied Analysis

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A New Grünwald-Letnikov Derivative Derived from a Second-Order Scheme

Abstract

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