Table 1 Computed maximum absolute errors for Example 1 by the proposed method on uniform mesh when \(\alpha = \frac{1}{12},\,\,\beta = \frac{5}{12}\)

\(10^{ - \,3}\)

2.9485e−04

2.0460e−05

1.3407e−06

8.5692e−08

5.4143e−09

3.4022e−10

\(10^{ - \,4}\)

1.5204e−02

1.4654e−03

1.0970e−04

7.4149e−06

4.8043e−07

3.0548e−08

\(10^{ - \,6}\)

6.0163e−01

3.6419e−01

1.4058e−01

2.8215e−02

3.1066e−03

2.4622e−04

\(10^{ - \,8}\)

9.5028e−01

9.0287e−01

8.1506e−01

6.6455e−01

4.4341e−01

2.0299e−01

\(10^{ - \,10}\)

9.9491e−01

9.8983e−01

9.7975e−01

9.5989e−01

9.2137e−01

8.4894e−01

\(10^{ - \,12}\)

9.9949e−01

9.9898e−01

9.9796e−01

9.9591e−01

9.9184e−01

9.8375e−01

\(10^{ - \,16}\)

9.9999e−01

9.9999e−01

9.9998e−01

9.9996e−01

9.9992e−01

9.9984e−01