Skip to main content

Theory and Modern Applications

Table 2 The discrete \(L^{2}\) errors, maximum errors, and convergence rates for scheme (8) for Example 1 with \(v_{1}=0.1\) and \(v_{2}=0.9\)

From: Two unconditionally stable difference schemes for time distributed-order differential equation based on Caputo–Fabrizio fractional derivative

h

τ

Δα

\(\Vert e^{N} \Vert ^{\#}_{\infty }\)

Order

\(\Vert e^{N} \Vert ^{\#}_{2}\)

Order

1/8

1/16

1/20

7.1433e−04

 

8.9705e−04

 

1/16

1/32

1/40

1.7223e−04

2.0523

2.1586e−04

2.0551

1/32

1/64

1/80

4.2569e−05

2.0165

5.3352e−05

2.0165

1/64

1/128

1/160

1.0500e−05

2.0194

1.3160e−05

2.0194

1/128

1/256

1/320

2.6233e−06

2.0009

3.2879e−06

2.0009