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Table 2 IVP ( 47 ), ( 48 ): Convergence of the collocation scheme, k=2

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

3.7e–03

3.7e–03

7.8e–03

1/4

5.1e–04

6.4e–01

2.87

1.6e–04

8.4e–02

4.50

1.2e–03

3.6e+00

2.73

1/8

6.6e–05

8.1e–01

2.96

8.1e–06

6.7e–02

4.34

1.5e–04

6.4e+00

2.93

1/16

8.3e–06

8.8e–01

2.99

4.4e–07

5.1e–02

4.21

2.0e–05

7.6e+00

2.98

1/32

1.0e–06

9.0e–01

3.00

2.5e–08

4.0e–02

4.12

2.5e–06

8.1e+00

2.99

1/64

1.3e–07

9.1e–01

3.00

1.5e–09

3.3e–02

4.06

3.1e–07

8.4e+00

3.00

1/128

1.6e–08

9.2e–01

3.00

9.3e–11

2.9e–02

4.03

3.8e–08

8.5e+00

3.00

1/256

2.0e–09

9.2e–01

3.00

5.7e–12

2.7e–02

4.02

4.8e–09

8.5e+00

3.00

1/512

2.6e–10

9.2e–01

3.00

3.5e–13

2.8e–02

4.03

6.0e–10

8.5e+00

3.00