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Theory and Modern Applications

Table 2 Problem 1 : Absolute errors 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

x

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

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

\(\boldsymbol {K=10^{6}} \)

Second order ( 2.7a )-( 2.7b )

Fourth order ( 2.21a )-( 2.21b )

Absolute error [ 17 ]

Second order ( 2.7a )-( 2.7b )

Fourth order ( 2.21a )-( 2.21b )

Absolute error [ 17 ]

Second order ( 2.7a )-( 2.7b )

Fourth order ( 2.21a )-( 2.21b )

Absolute error [ 17 ]

0.0

0.0e+00

0.0e+00

0.0e+00

0.0e+00

0.0e+00

0.0e+00

0.0e+00

0.0e+00

0.0e+00

0.1

9.2e−06

7.9e−09

1.2e−11

2.4e−05

1.8e−08

1.5e−14

6.9e−04

2.1e−08

1.5e−10

0.2

2.7e−05

2.0e−08

4.0e−11

4.9e−05

3.4e−08

2.9e−13

3.8e−05

3.6e−08

3.7e−08

0.3

4.4e−05

3.3e−08

8.5e−11

7.0e−05

4.8e−08

3.1e−12

7.2e−04

4.8e−08

9.0e−07

0.4

5.8e−05

4.2e−08

1.6e−10

8.7e−05

5.8e−08

1.9e−11

7.0e−05

2.1e−10

8.5e−06

0.5

6.6e−05

4.7e−08

2.9e−10

9.8e−05

6.4e−08

7.4e−11

7.5e−04

5.7e−08

4.8e−05

0.6

6.7e−05

4.6e−08

5.1e−10

1.0e−04

6.4e−08

2.0e−10

8.5e−05

6.3e−08

1.9e−04

0.7

5.8e−05

3.9e−08

7.4e−10

9.5e−05

5.7e−08

3.9e−10

7.7e−04

5.7e−08

6.4e−04

0.8

4.0e−05

2.5e−08

8.1e−10

7.8e−05

4.1e−08

5.1e−10

6.7e−05

4.3e−08

1.7e−03

0.9

1.5e−05

8.5e−09

4.7e−10

4.5e−05

1.5e−08

3.4e−10

7.7e−04

2.0e−08

4.2e−03

1.0

0.0e+00

0.0e+00

0.0e+00

0.0e+00

0.0e+00

0.0e+00

0.0e+00

0.0e+00

0.0e+00