Journal
BIT NUMERICAL MATHEMATICS
Volume 54, Issue 2, Pages 555-584Publisher
SPRINGER
DOI: 10.1007/s10543-013-0443-3
Keywords
Fractional differential equation; Finite difference method; Caputo fractional derivative; Error estimates
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In this paper we introduce higher order numerical methods for solving fractional differential equations. We use two approaches to this problem. The first approach is based on a direct discretisation of the fractional differential operator: we obtain a numerical method for solving a linear fractional differential equation with order 0 < 1. The order of convergence of the numerical method is O(h (3-alpha) ). Our second approach is based on discretisation of the integral form of the fractional differential equation and we obtain a fractional Adams-type method for a nonlinear fractional differential equation of any order alpha > 0. The order of convergence of the numerical method is O(h (3)) for alpha a parts per thousand yen1 and O(h (1+2 alpha) ) for 0
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