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Theory and Modern Applications

Table 17 Problem 7 : MAEs and RMSEs using ( 2.7a )-( 2.7b ) and ( 2.21a )-( 2.21b )

From: A class of quasi-variable mesh methods based on off-step discretization for the solution of non-linear fourth order ordinary differential equations with Dirichlet and Neumann boundary conditions

N

 

Second order ( C  = 0.45)

Third order ( C  = 1.1)

 

MAE

RMSE

MAE

RMSE

10

u

2.3524e−06

1.2294e−06

3.3425e−09

2.1271e−09

\(u' \)

1.6070e−05

6.8720e−06

1.5594e−08

1.0533e−08

v

1.2026e−05

8.0087e−06

1.9955e−08

1.2704e−08

\(v' \)

3.9650e−05

2.8558e−05

1.0046e−07

5.9011e−08

20

u

7.4405e−07

3.8633e−07

1.5475e−09

1.0102e−09

\(u'\)

4.0111e−06

1.9062e−06

4.8890e−09

3.5842e−09

v

3.0216e−06

1.9569e−06

3.8218e−09

2.4468e−09

\(v' \)

9.9398e−06

6.9784e−06

1.3573e−08

8.9719e−09

40

u

1.9760e−07

1.0079e−07

2.7490e−10

1.7786e−10

\(u'\)

1.0611e−06

4.8541e−07

8.6380e−10

6.1758e−10

v

7.5983e−07

4.8342e−07

5.2919e−10

3.3868e−10

\(v' \)

2.4813e−06

1.7237e−06

1.7523e−09

1.1953e−09

Order

u

1.9128

1.9385

2.49

2.51

\(u'\)

1.9185

1.9734

2.50

2.54

v

1.9916

2.0172

2.85

2.85

\(v' \)

2.0021

2.0173

2.95

2.91