Table 2 (Example 4.2) Maximum absolute errors and convergence orders

\(\frac{\pi}{20}\)

7.10e − 03

7.19e − 03

7.30e − 03

7.46e − 03

\(\frac{\pi}{40}\)

1.86e − 03

1.93

1.88e − 03

1.94

1.91e − 03

1.93

1.96e − 03

1.93

\(\frac{\pi}{80}\)

4.76e − 04

1.97

4.82e − 04

1.96

4.90e − 04

1.96

5.02e − 04

1.97

\(\frac{\pi}{160}\)

1.21e − 04

1.98

1.22e − 04

1.98

1.24e − 04

1.98

1.27e − 04

1.98

\(\frac{\pi}{320}\)

3.03e − 05

2.00

3.07e − 05

1.99

3.12e − 05

1.99

3.19e − 05

1.99

\(\frac{\pi}{20}\)

8.43e − 03

7.91e − 02

1.32e − 02

1.31e − 02

\(\frac{\pi}{40}\)

2.12e − 03

1.99

1.98e − 02

2.00

3.69e − 03

1.84

3.67e − 03

1.84

\(\frac{\pi}{80}\)

5.30e − 04

2.00

4.93e − 03

2.01

9.71e − 04

1.93

9.66e − 04

1.93

\(\frac{\pi}{160}\)

1.33e − 04

1.99

1.23e − 03

2.00

2.49e − 04

1.96

2.47e − 04

1.97

\(\frac{\pi}{320}\)

3.32e − 05

2.00

3.07e − 04

2.00

6.30e − 05

1.98

6.26e − 05

1.98

\(\frac{\pi}{20}\)

1.30e − 02

1.29e − 02

1.36e − 02

\(\frac{\pi}{40}\)

3.64e − 03

1.84

3.61e − 03

1.84

3.55e − 03

1.94

\(\frac{\pi}{80}\)

9.59e − 04

1.92

9.48e − 04

1.93

9.33e − 04

1.93

\(\frac{\pi}{160}\)

2.46e − 04

1.96

2.43e − 04

1.96

2.39e − 04

1.96

\(\frac{\pi}{320}\)

6.21e − 05

1.99

6.14e − 05

1.98

6.04e − 05

1.98