Theory and Modern Applications
Table 1 Accuracy of Legendre spectral derivative of the different orders for two functions \((x+1)^{\alpha-1}\) and \(J_{0}(2\sqrt{x})\)
From: Fractional spectral differentiation matrices based on Legendre approximation
N | \(D^{\alpha}[(x+1)^{\alpha-1}]\) | \(D^{\alpha}[J_{0}(2\sqrt{x})]\) | ||||
|---|---|---|---|---|---|---|
α = 0.25 | α = 0.50 | α = 0.75 | α = 0.25 | α = 0.50 | α = 0.75 | |
5 | 1.34×10−4 | 2.31×10−4 | 2.34×10−4 | 1.30×10−7 | 5.64×10−7 | 1.72×10−6 |
10 | 2.00×10−8 | 3.69×10−8 | 4.13×10−8 | 8.88×10−16 | 8.88×10−16 | 2.77×10−15 |
15 | 3.00×10−12 | 5.68×10−12 | 6.79×10−12 | |||
20 | 7.77×10−16 | 2.55×10−15 | 2.02×10−15 | |||