*3.2. Convergence of HAM Solutions*

To obtain the values of auxiliary parameters *h*1, *h*<sup>2</sup> and *h*3, h-curves against ψ-- , φ- and θ are prepared and the results are given in Figures 2–4. Convergence intervals lie in the flat portion of these h-curves as witnessed from plots. It is observed those permissible values of h1, h2 and h3 up to the 10th order of approximation are: −0.1 ≤ h1 ≤ 0.3, −0.12 ≤ h2 ≤ 0.01, −0.2 ≤ h3 ≤ 0.05.

**Figure 2.** *h*-curve for the ψ at z = 1, Q = 2, ε = 0.2.

**Figure 3.** *h*-curve for the φ at z = 1, Q = 2, ε = 0.2.

**Figure 4.** *h*-curve for the θ at z = 1, Q = 2, ε = 0.2.
