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Theory and Modern Applications

Table 3 The PW-AE for Example 2 at \(M=10\) and \(\delta =0.5\)

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

x

SU-pseudo-GM

NNM

IRBF

DRBF

S

ν

[41]

[42]

[42]

−0.49

0.49

1

0.1

\(S_{1}\)

2.2e-05

2.2e-05

2.2e-05

3.4e-03

1.5e-05

2.8e-05

\(S_{2}\)

7.8e-07

1.6e-06

7.7e-07

0.2

\(S_{1}\)

1.3e-05

1.3e-05

1.3e-05

8.7e-03

8.5e-06

2.0e-05

\(S_{2}\)

2.5e-06

1.3e-06

3.0e-07

0.3

\(S_{1}\)

1.0e-05

1.0e-05

1.0e-05

1.1e-02

–

–

\(S_{2}\)

2.3e-07

1.5e-06

1.1e-06

0.4

\(S_{1}\)

8.7e-06

8.7e-06

8.7e-06

8.1e-03

–

–

\(S_{2}\)

1.2e-06

2.8e-06

2.1e-06

0.5

\(S_{1}\)

7.5e-06

7.5e-06

7.5e-06

4.2e-04

4.7e-06

6.7e-06

\(S_{2}\)

9.8e-07

1.7e-06

1.1e-06

0.6

\(S_{1}\)

6.4e-06

6.4e-06

6.4e-06

7.8e-03

4.8e-06

6.8e-06

\(S_{2}\)

2.2e-08

1.1e-06

5.4e-07

0.7

\(S_{1}\)

5.3e-06

5.3e-06

5.3e-06

9.1e-03

–

–

\(S_{2}\)

7.8e-07

2.1e-06

1.5e-06

0.8

\(S_{1}\)

4.2e-06

4.2e-06

4.2e-06

1.4e-03

–

–

\(S_{2}\)

3.6e-07

1.7e-06

1.3e-06

0.9

\(S_{1}\)

3.3e-06

3.3e-06

3.3e-06

1.6e-02

1.5e-06

1.2e-05

\(S_{2}\)

2.3e-07

1.2e-06

1.2e-06

1

\(S_{1}\)

1.9e-06

1.9e-06

1.9e-06

5.6e-03

2.0e-06

7.0e-06

\(S_{2}\)

1.5e-07

1.4e-06

3.3e-06