Table 1 (Example 4.1) Maximum absolute errors

Mid-knot cubic non-polynomial spline α = 1/8, β = 3/8

2.40e − 04

6.34e − 05

1.63e − 05

Mid-knot cubic non-polynomial spline α = 1/10, β = 2/5

3.44e − 04

9.11e − 05

2.34e − 05

Mid-knot cubic non-polynomial spline α = 1/12, β = 5/12

4.14e − 04

1.09e − 04

2.81e − 05

Mid-knot cubic non-polynomial spline α = 1/14, β = 3/7

4.64e − 04

1.23e − 04

3.15e − 05

Mid-knot cubic non-polynomial spline α = 1/16, β = 7/16

5.01e − 04

1.33e − 04

3.40e − 05

Parametric cubic spline [12] α = 1/8, β = 3/8

8.62e − 04

2.47e − 04

6.57e − 05

Parametric cubic spline [12] α = 1/10, β = 2/5

7.74e − 04

2.21e − 04

5.89e − 05

Parametric cubic spline [12] α = 1/12, β = 5/12

7.16e − 04

2.04e − 04

5.43e − 05

Parametric cubic spline [12] α = 1/14, β = 3/7

6.74e − 04

1.92e − 04

5.11e − 05

Parametric cubic spline [12, 25] α = 1/16, β = 7/16

6.43e − 04

1.83e − 04

4.87e − 05

Deficient discrete cubic spline [8]

1.19e − 03

3.04e − 04

7.68e − 05

Cubic spline [3]

1.26e − 03

3.29e − 04

8.43e − 05

Modified Numerov method [4]

1.65e − 03

4.33e − 04

1.11e − 04

Cubic spline [2]

1.94e − 03

4.99e − 04

1.27e − 04

Quadratic spline [1]

2.20e − 03

5.87e − 04

1.51e − 04

Quintic spline [6]

2.57e − 03

7.31e − 04

1.94e − 04

Collocation-cubic B spline [19]

1.40e − 02

7.71e − 03

4.04e − 03

Cubic spline [5]

1.80e − 02

9.13e − 03

4.60e − 03

Quintic spline [5]

1.82e − 02

9.17e − 03

4.61e − 03

Numerov [22]

2.32e − 02

1.21e − 02

6.17e − 03

Finite difference scheme [22]

2.50e − 02

1.29e − 02

6.58e − 03