A New Grünwald-Letnikov Derivative Derived from a Second-Order Scheme. (26th August 2015)

• Record Type: Journal Article
• Authors: Jacobs, B. A.
• Other Names: Xia Tiecheng Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2015(2015)
• Publication Date: 2015-08-26
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2015/952057
• Languages: English
• ISSNs: 1085-3375

Abstract

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.