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Theory and Modern Applications

Table 1 The MAE for Example 1

From: Shifted ultraspherical pseudo-Galerkin method for approximating the solutions of some types of ordinary fractional problems

c

M

SU-pseudo-GM

[39]

[40]

S

ν

−0.49

0.49

1

1

8

\(S_{1}\)

6.2e-08

6.2e-08

6.2e-08

6.2e-03

2.0e-12

\(S_{2}\)

2.5e-08

4.3e-08

3.1e-08

16

\(S_{1}\)

4.9e-15

1.2e-14

4.9e-15

7.5e-04

4.0e-14

\(S_{2}\)

2.7e-15

2.2e-15

1.3e-15

32

\(S_{1}\)

3.1e-15

6.5e-13

1.9e-12

1.0e-04

2.0e-11

\(S_{2}\)

2.7e-15

2.2e-15

1.3e-15

6

16

\(S_{1}\)

6.3e-06

6.3e-06

6.3e-06

8.4e-03

1.0e-08

\(S_{2}\)

2.1e-07

3.6e-07

2.0e-07

32

\(S_{1}\)

6.9e-10

1.4e-08

1.3e-09

7.5e-04

2.0e-08

\(S_{2}\)

9.4e-11

5.1e-09

3.5e-11