Skip to main content

Theory and Modern Applications

Table 2 The maximum absolute errors for Example  2 for different values of ε

From: A fitted numerical scheme for second order singularly perturbed delay differential equations via cubic spline in compression

ε ↓∖ N →

32

64

128

256

512

1,024

2−5

5.155E − 04

1.465E − 04

3.789E − 05

9.552E − 06

2.403E − 06

8.200E − 07

2−6

7.592E − 04

2.664E − 04

7.515E − 05

1.945E − 05

4.911E − 06

1.202E − 06

2−7

8.368E − 04

3.857E − 04

1.353E − 04

3.818E − 05

9.876E − 06

2.470E − 06

2−8

8.409E − 04

4.251E − 04

1.944E − 04

6.821E − 05

1.924E − 05

4.963E − 06

2−9

8.409E − 04

4.272E − 04

2.143E − 04

9.756E − 05

3.425E − 05

9.658E − 06

2−10

8.409E − 04

4.272E − 04

2.153E − 04

1.075E − 04

4.892E − 05

1.717E − 05

2−11

8.409E − 04

4.272E − 04

2.153E − 04

1.081E − 04

5.387E − 05

2.450E − 05

2−12

8.409E − 04

4.272E − 04

2.153E − 04

1.081E − 04

5.414E − 05

2.694E − 05

2−13

8.409E − 04

4.272E − 04

2.153E − 04

1.081E − 04

5.414E − 05

2.707E − 05

2−14

8.409E − 04

4.272E − 04

2.153E − 04

1.081E − 04

5.414E − 05

2.707E − 05

2−15

8.409E − 04

4.272E − 04

2.153E − 04

1.081E − 04

5.414E − 05

2.707E − 05

2−16

8.409E − 04

4.272E − 04

2.153E − 04

1.081E − 04

5.414E − 05

2.707E − 05

2−17

8.409E − 04

4.272E − 04

2.153E − 04

1.081E − 04

5.414E − 05

2.707E − 05

2−18

8.409E − 04

4.272E − 04

2.153E − 04

1.081E − 04

5.414E − 05

2.707E − 05

2−19

8.409E − 04

4.272E − 04

2.153E − 04

1.081E − 04

5.414E − 05

2.707E − 05

2−20

8.409E − 04

4.272E − 04

2.153E − 04

1.081E − 04

5.414E − 05

2.707E − 05

\(E^{N}\)

8.409E − 04

4.272E − 04

2.153E − 04

1.081E − 04

5.414E − 05

2.707E − 05

\(R^{N}\)

9.769E − 01

9.885E − 01

9.947E − 01

9.969E − 01

9.998E − 01

8.436E − 01