Table 5 Comparison of the values of \(\beta =\varUpsilon ^{\frac{1}{2}}\), \(f''(0)\), \(\theta (1)\), and \(-\theta '(0)\) using 20th-order HAM via Mathematica package BVPh2.0 approximation and shooting method for the case \(\lambda =0.2\), \(I_{0}=0\), \(A=0.3\), \(N=0.2\), \(S=0.4\), \(\mathit{Ma}=1\), \(M=1\), \(\mathit{Pr} =1\) and several values of β

β

β

\(f''(0)\)

θ(1)

\(-\theta '(0)\)

β

\(f''(0)\)

θ(1)

\(-\theta '(0)\)