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Table 3 Show Individual residual square error and OHAM solutions convergence at various approximation orders when \(M = Pp = 1 = 2 = \beta = 1,Fs = \delta = \delta_{1} = \delta_{2} = 0.5,\hbar_{u} = - 0.82706,\hbar_{{\uptheta }} = - 0.75851,\hbar_{\phi } = - 0.96084\)

From: Chemical entropy generation and second-order slip condition on hydrodynamic Casson nanofluid flow embedded in a porous medium: a fast convergent method

m \({\Delta }_{m}^{f}\) \({\Delta }_{m}^{\theta }\) \({\Delta }_{m}^{\phi }\) \(f^{\prime \prime } \left( 0 \right)\) \(- \theta {^{\prime}}\left( 0 \right)\) \(- \phi {^{\prime}}\left( 0 \right)\) CPU time (s)
2 \(1.79 \times 10^{ - 3}\) \(2.64 \times 10^{ - 6}\) \(2.68 \times 10^{ - 8}\) 2.289542 0.137041 0.011381 0.3437448
4 \(2.54 \times 10^{ - 8}\) \(1.65 \times 10^{ - 7}\) \(1.14 \times 10^{ - 13}\) 2.273865 0.13685 0.011487 0.7187314
6 \(2.35 \times 10^{ - 11}\) 4.85 \(\times 10^{ - 11}\) \(9.47 \times 10^{ - 15}\) 2.274001 0.137146 0.011488 1.1405919
8 \(1.54 \times 10^{ - 12}\) \(1.03 \times 10^{ - 13}\) \(2.26 \times 10^{ - 17}\) 2.274003 0.137151 0.011488 1.671824
10 \(8.95 \times 10^{ - 17}\) \(4.03 \times 10^{ - 17}\) \(6.25 \times 10^{ - 20}\) 2.274004 0.137151 0.011488 2.3905487
12 \(9.20 \times 10^{ - 19}\) \(3.19 \times 10^{ - 19}\) \(5.55 \times 10^{ - 23}\) 2.274004 0.137151 0.011488 3.3280166
14 \(2.09 \times 10^{ - 22}\) \(4.05 \times 10^{ - 22}\) \(1.32 \times 10^{ - 25}\) 2.274004 0.137151 0.011488 3.7185883
20 \(7.76 \times 10^{ - 24}\) \(1.41 \times 10^{ - 24}\) \(2.63 \times 10^{ - 28}\) 2.274004 0.137151 0.011488 12.1245886
26 \(6.19 \times 10^{ - 27}\) \(1.60 \times 10^{ - 27}\) \(8.66 \times 10^{ - 31}\) 2.274004 0.137151 0.011488 18.2174761
30 \(2.46 \times 10^{ - 29}\) \(5.56 \times 10^{ - 30}\) \(1.37 \times 10^{ - 33}\) 2.274004 0.137151 0.011488 22.3578236