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Table 4 Numerical results for Example 3

From: A fast multiscale Galerkin algorithm for solving boundary value problem of the fractional Bagley–Torvik equation

n

x(n)

\(\|u^{*}-\tilde{u}_{n}\|_{1}\)

C.O.

\(\|u^{*}-\tilde {u}_{n}\|_{2}\)

C.O.

\(\|u^{*}-\tilde{u}_{n}\|_{\infty}\)

C.O.

C.R.

T

3

7

2.3740e-2

 

9.2810e-4

 

3.3646e-3

 

77.6%

<0.01

4

15

1.2346e-2

0.94328

2.4402e-4

1.9273

9.5997e-4

1.8094

62.2%

0.01

5

31

6.2333e-3

0.98597

6.2106e-5

1.9742

2.7120e-4

1.8236

44.3%

0.04

6

63

3.1242e-3

0.99651

1.5368e-5

2.0148

6.1689e-5

2.1363

29.3%

0.12

7

127

1.5630e-3

0.99913

3.8719e-6

1.9888

1.7795e-5

1.7935

18.5%

0.29

8

255

7.8164e-4

0.99978

9.9052e-7

1.9668

3.3084e-6

2.5501

11.2%

0.73

9

511

3.9084e-4

0.99994

2.8535e-7

1.7954

1.0062e-6

1.5944

6.69%

2.03