Skip to main content

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 = 0.25α = 0.50α = 0.75α = 0.25α = 0.50α = 0.75
51.34×10−42.31×10−42.34×10−41.30×10−75.64×10−71.72×10−6
102.00×10−83.69×10−84.13×10−88.88×10−168.88×10−162.77×10−15
153.00×10−125.68×10−126.79×10−12   
207.77×10−162.55×10−152.02×10−15