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Table 3 IVP ( 47 ), ( 48 ): Convergence of the collocation scheme, k=3

From: On linear ODEs with a time singularity of the first kind and unsmooth inhomogeneity

h

Equidistant points

Gaussian points

Uniform

Mesh

Uniform

Y h Y

c

p

Y h Y

c

p

Y h Y

c

p

1/2

2.0e–04

3.6e–05

−−

3.5e–04

1/4

7.4e–06

3.8e+00

4.75

5.1e–07

2.6e–03

6.15

1.3e–05

2.8e+02

4.73

1/8

3.0e–07

2.7e+00

4.63

7.6e–09

2.3e–03

6.07

5.4e–07

1.8e+02

4.61

1/16

1.4e–08

1.5e+00

4.46

1.2e–10

2.1e–03

6.03

2.5e–08

9.1e+01

4.44

1/32

6.9e–10

8.0e–01

4.30

1.8e–12

2.1e–03

6.02

1.3e–09

4.2e+01

4.29

1/64

3.8e–11

4.4e–01

4.18

2.0e–14

8.9e–03

6.44

7.1e–11

2.1e+01

4.17

1/128

2.2e–12

2.8e–01

4.10

3.4e–14

1.0e–15

−0.72

4.2e–12

1.3e+01

4.09

1/256

1.3e–13

2.0e–01

4.04

1.1e–14

1.1e–10

1.66

2.5e–13

8.5e+00

4.03

1/512

7.1e–15

8.0e–01

4.24

2.0e–14

5.9e–17

−0.94

1.6e–14

8.7e+00

4.03