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