Theory and Modern Applications
Table 3 The comparative study of \(\operatorname{Re}{[\mathcal {W}_{(3)}]}\) solutions of δ-HPTM, q-HATM, and exact solution for Example 2 at \(\beta_{1}=1, \beta_{2}=2, \beta_{3}=0.1, y=2, z=2, \xi=0.1, e_{0}=1, p=0.8, q=0.8, \phi=1\), and \(t=0.01\)
x | Exact | δ-HPTM (δ = 1) | q-HPTM (n = 1,ħ = 1) | ||
|---|---|---|---|---|---|
Approx | Absolute error | Approx | Absolute error | ||
−15 | 0.9801926018 | 0.9801926018 | 5.551115 × 10−15 | 0.9801926018 | 5.551115 × 10−15 |
−10 | 0.9642322805 | 0.9642322805 | 6.294965 × 10−14 | 0.9642322805 | 6.294965 × 10−14 |
−5 | 0.9591394126 | 0.9591394126 | 1.930678 × 10−13 | 0.9591394126 | 1.930678 × 10−13 |
0 | 1.0156139368 | 1.0156139368 | 2.708944 × 10−13 | 1.0156139368 | 2.708944 × 10−13 |
5 | 1.0435482789 | 1.0435482789 | 4.729550 × 10−14 | 1.0435482789 | 4.729550 × 10−14 |
10 | 1.0279075447 | 1.0279075447 | 2.753353 × 10−14 | 1.0279075447 | 2.753353 × 10−14 |
15 | 1.0150065850 | 1.0150065850 | 2.220446 × 10−16 | 1.0150065850 | 2.220446 × 10−16 |