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Table 4 Order [m, m] ISHAM approximate results for the velocity profile f' (η) of the MHD boundary layer flow (Example 3) when M = 10 using L = 10, ħ = -1 and N = 200

From: An improved spectral homotopy analysis method for solving boundary layer problems

η

f' (η)

Exact

Absolute error

 

[1,1]

[2,2]

[3,3]

 

[1,1]

[2,2]

[3,3]

0.0

1.00000000

1.00000000

1.00000000

1.00000000

0.00000000

0.00000000

0.00000000

0.5

0.19106051

0.19046007

0.19046007

0.19046013

0.00060038

0.00000006

0.00000006

1.0

0.03731355

0.03627506

0.03627506

0.03627506

0.00103849

0.00000000

0.00000000

1.5

0.00795438

0.00690893

0.00690893

0.00690895

0.00104543

0.00000002

0.00000002

2.0

0.00212716

0.00131588

0.00131588

0.00131588

0.00081128

0.00000000

0.00000000

2.5

0.00080280

0.00025062

0.00025062

0.00025062

0.00055218

0.00000000

0.00000000

3.0

0.00040021

0.00004773

0.00004773

0.00004773

0.00035248

0.00000000

0.00000000

3.5

0.00022752

0.00000909

0.00000909

0.00000909

0.00021843

0.00000000

0.00000000

4.0

0.00013536

0.00000173

0.00000173

0.00000173

0.00013363

0.00000000

0.00000000

5.0

0.00004944

0.00000006

0.00000006

0.00000006

0.00004938

0.00000000

0.00000000

6.0

0.00001818

0.00000000

0.00000000

0.00000000

0.00001818

0.00000000

0.00000000