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Theory and Modern Applications

Table 4 Problem 3 : MAEs using ( 2.7a )-( 2.7b ) with \(\pmb{C=1}\)

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

λ

1

10

\(\boldsymbol {10^{2}} \)

\(\boldsymbol {10^{3}} \)

\(\boldsymbol {10^{4}} \)

N

u

\(\boldsymbol {u'} \)

u

\(\boldsymbol {u'} \)

u

\(\boldsymbol {u'} \)

u

\(\boldsymbol {u'} \)

u

\(\boldsymbol {u'} \)

8

7.11e−07

2.36e−05

1.61e−04

1.21e−03

5.25e−03

3.95e−02

3.48e−02

2.57e−01

1.29e−01

7.07e−01

16

4.61e−07

3.84e−06

4.46e−05

3.03e−04

1.31e−03

9.53e−03

7.96e−03

1.19e−01

3.89e−02

4.31e−01

32

1.36e−07

8.95e−07

1.15e−05

7.85e−05

3.27e−04

2.27e−03

1.94e−03

3.21e−02

7.36e−03

2.48e−01

64

3.51e−08

2.42e−07

2.90e−06

1.98e−05

8.21e−05

5.69e−04

4.84e−04

7.28e−03

1.83e−03

8.49e−02

128

8.86e−09

6.16e−08

7.27e−07

4.96e−06

2.05e−05

1.42e−04

1.21e−04

1.78e−03

4.58e−04

1.94e−02

256

2.29e−09

1.50e−08

1.82e−07

1.24e−06

5.13e−06

3.55e−05

3.03e−05

4.43e−04

1.14e−04

4.60e−03

Order

1.95

2.04

2.00

2.00

2.00

2.00

2.00

2.01

2.00

2.08