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Table 9 Transformed TVP ( 50 ): 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

2.2e+00

1.5e–01

1.5e–01

1/4

2.8e–01

1.1e+03

2.98

3.7e–03

5.7e+00

5.29

4.1e–03

4.5e+05

5.18

1/8

2.1e–02

8.2e+03

3.71

8.3e–05

7.5e+00

5.49

8.3e–05

2.1e+06

5.62

1/16

1.4e–03

1.7e+04

3.93

5.2e–06

3.4e–01

4.00

5.2e–06

2.1e+03

4.00

1/32

8.8e–05

2.2e+04

3.98

3.3e–07

3.4e–01

4.00

3.3e–07

2.1e+03

4.00

1/64

5.5e–06

2.3e+04

4.00

2.0e–08

3.4e–01

4.00

2.0e–08

2.1e+03

4.00

1/128

3.5e–07

2.4e+04

4.00

1.3e–09

3.4e–01

4.00

1.3e–09

2.1e+03

4.00

1/256

2.2e–08

2.4e+04

4.00

8.0e–11

3.3e–01

3.99

8.0e–11

2.0e+03

3.99

1/512

1.4e–09

2.4e+04

4.00

7.0e–12

2.2e–02

3.50

7.0e–12

4.6e+01

3.50