Table 2 Absolute residual error values of \(y_{{s4,M}}(t)\) with \(s=1,2\) and \(N=4\) and \(M=5, 6 \) at some points (for comparison, one can see [44])

0

1.8532e − 01

3.4677e − 01

7.6478e − 01

7.9220e − 03

1.4726e − 02

3.1173e − 03

0.5

1.2514e − 01

1.2920e − 01

3.4068e − 01

2.1792e − 03

2.6024e − 04

9.5723e − 04

1

7.5154e − 02

3.4368e − 02

1.3965e − 01

1.6174e − 03

1.5337e − 03

8.3699e − 04

1.5

3.8252e − 02

4.1932e − 03

4.8231e − 02

2.2729e − 03

2.7637e − 04

7.1159e − 04

2

1.3902e − 02

1.8065e − 03

1.1406e − 02

1.1969e − 03

1.8752e − 05

9.6725e − 04

2.5

8.0535e − 11

1.8300e − 03

1.5884e − 10

2.6391e − 11

2.8032e − 04

7.7868e − 09

3

5.8527e − 03

7.5528e − 04

1.5773e − 03

5.0326e − 04

2.2769e − 04

7.8870e − 04

3.5

5.8543e − 03

5.9818e − 04

5.6770e − 04

3.6513e − 04

2.0922e − 04

4.5973e − 04

4

2.2951e − 03

1.1248e − 03

3.9443e − 04

7.3925e − 05

3.7841e − 04

3.9797e − 04

4.5

1.5116e − 03

6.3471e − 05

2.6966e − 04

5.3039e − 06

1.8942e − 05

2.6853e − 04

5

8.6549e − 11

2.1856e − 10

1.3063e − 09

2.3356e − 11

4.1398e − 10

2.0789e − 04