Theory and Modern Applications
Table 6 The comparative study of \(\operatorname{Im}{[\mathcal {W}_{(3)}]}\) solutions of δ-HPTM, q-HATM, and exact solution for Example 3 at \(\beta_{1}=1, \beta_{2}=2, \beta_{3}=10, y=2, z=2, \xi=1, e_{0}=3, p=0.3, q=0.3\), and \(t=0.01\)
x | Exact | δ-HPTM (δ = 1) | q-HPTM (n = 1,ħ = 1) | ||
|---|---|---|---|---|---|
Approx | Absolute error | Approx | Absolute error | ||
−15 | −0.9227631870 | −0.9227631870 | 7.371881 × 10−14 | −0.9227631870 | 7.371881 × 10−14 |
−10 | −0.2891329576 | −0.2891329576 | 3.064215 × 10−14 | −0.2891329576 | 3.064215 × 10−14 |
−5 | −1.0474742139 | −1.0474742140 | 1.303402 × 10−13 | −1.0474742140 | 1.303402 × 10−13 |
0 | −0.2754234881 | −0.2754234881 | 3.419487 × 10−14 | −0.2754234881 | 3.419487 × 10−14 |
5 | −1.1689377811 | −1.1689377811 | 1.636469 × 10−13 | −1.1689377811 | 1.636469 × 10−13 |
10 | −0.2859219243 | −0.2859219243 | 2.742251 × 10−14 | −0.2859219243 | 2.742251 × 10−14 |
15 | −1.2662691579 | −1.2662691579 | 5.351275 × 10−14 | −1.2662691579 | 5.351275 × 10−14 |