Table 4 Comparison of LHPM and HPM results in case of negative \({S}_{q}\) when \(\alpha =4.0\), \({M}_{g}={M}_{p}=0.5,\beta =0.05\).
From: Fractional analysis of unsteady squeezing flow of Casson fluid via homotopy perturbation method
Parameter | \(\eta\) | Solution | Residual error | ||
|---|---|---|---|---|---|
HPM56 | LHPM | HPM56 | LHPM | ||
\({S}_{q}=-0.2\) | \(0.1\) | \(0.14944\) | \(0.14944\) | \(9.93\times 1{0}^{-11}\) | \(4.35\times 1{0}^{-16}\) |
\(0.3\) | \(0.43635\) | \(0.43635\) | \(5.16\times 1{0}^{-10}\) | \(9.73\times 1{0}^{-13}\) | |
\(0.5\) | \(0.68732\) | \(0.68732\) | \(5.33\times 1{0}^{-10}\) | \(3.56\times 1{0}^{-11}\) | |
\(0.7\) | \(0.87838\) | \(0.87838\) | \(1.53\times 1{0}^{-9}\) | \(3.82\times 1{0}^{-10}\) | |
\(0.9\) | \(0.98547\) | \(0.98547\) | \(1.17\times 1{0}^{-9}\) | \(2.25\times 1{0}^{-9}\) | |
\({S}_{q}=-0.6\) | \(0.1\) | \(0.14955\) | \(0.14955\) | \(1.24\times 1{0}^{-8}\) | \(3.06\times 1{0}^{-15}\) |
\(0.3\) | \(0.43664\) | \(0.43664\) | \(3.79\times 1{0}^{-8}\) | \(5.95\times 1{0}^{-12}\) | |
\(0.5\) | \(0.68765\) | \(0.68765\) | \(7.21\times 1{0}^{-8}\) | \(1.78\times 1{0}^{-10}\) | |
\(0.7\) | \(0.87859\) | \(0.87859\) | \(1.42\times 1{0}^{-7}\) | \(1.47\times 1{0}^{-9}\) | |
\(0.9\) | \(0.98556\) | \(0.98551\) | \(3.01\times 1{0}^{-7}\) | \(6.26\times 1{0}^{-9}\) | |
