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Theory and Modern Applications

Table 6 Problem 3 : MAEs using ( 2.21a )-( 2.21b ) 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

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

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

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

N

u

\(\boldsymbol {u'}\)

u

\(\boldsymbol {u'}\)

u

\(\boldsymbol {u'}\)

8

1.17e−05

9.57e−05

3.89e−04

4.67e−03

3.03e−03

2.43e−02

16

8.21e−07

6.06e−06

4.25e−05

6.63e−04

6.87e−04

1.37e−02

32

5.27e−08

3.67e−07

3.02e−06

4.94e−05

8.75e−05

2.98e−03

64

3.33e−09

2.31e−08

1.95e−07

2.93e−06

6.84e−06

3.08e−04

128

2.14e−10

1.46e−09

1.23e−08

1.81e−07

4.55e−07

1.90e−05

Order

3.96

3.98

3.99

4.02

3.91

4.01