Table 1 Estimating individual error for different order of approximations with fixed values of \(S_q=1.0\), \(\Omega =2\), \(D_u=0.2\), \(P_r=0.1\), \( S_c=0.1 \), \( S_r=1 \), \( S=0.5\), \( M=0.5 \), \(R_d=1\), \(E_c=0.2 \), and \(\delta =0.1\).

1

0.34078

0.0214375

0.00306542

0.0000362193

5

1.31385 \(\times 10^{-9}\)

4.69349 \(\times 10^{-10}\)

8.19172\(\times 10^{-12}\)

1.95769\(\times 10^{-13}\)

10

1.24169\(\times 10^{-19}\)

2.19766\(\times 10^{-19}\)

3.13303\(\times 10^{-21}\)

3.46306 \(\times 10^{-23}\)

15

1.9463\(\times 10^{-29}\)

9.53779 \(\times 10^{-29}\)

2.27437\(\times 10^{-30}\)

2.41344 \(\times 10^{-32}\)

20

2.95105\(\times 10^{-30}\)

6.59002\(\times 10^{-31}\)

7.44284\(\times 10^{-31}\)

8.3872\(\times 10^{-35}\)

25

2.98353\(\times 10^{-30}\)

6.18862\(\times 10^{-31}\)

7.44284\(\times 10^{-31}\)

7.35201\(\times 10^{-35}\)

30

2.97169\(\times 10^{-30}\)

6.18015\(\times 10^{-31}\)

7.44284\(\times 10^{-31}\)

6.48534\(\times 10^{-35}\)

35

3.33562\(\times 10^{-30}\)

6.06028\(\times 10^{-31}\)

7.44284\(\times 10^{-31}\)

5.32979\(\times 10^{-35}\)

40

2.95894\(\times 10^{-30}\)

6.55782\(\times 10^{-31}\)

7.44284\(\times 10^{-31}\)

6.48534\(\times 10^{-35}\)