Theory and Modern Applications
Table 5 The comparative study of \(\operatorname{Re}{[\mathcal {W}_{(3)}]}\) solutions of δ-HPTM, q-HATM, and exact solution for Example 3 at \(\beta_{1}=1, \beta_{2}=2, \beta_{3}=10, y=2, z=2, \xi=1, e_{0}=3, p=0.3, q=0.3, \phi=1\), and \(t=0.01\)
x | Exact | δ-HPTM (δ = 1) | q-HPTM (n = 1,ħ = 1) | ||
|---|---|---|---|---|---|
Approx | Absolute error | Approx | Absolute error | ||
−15 | 0.2924916343 | 0.2924916343 | 2.881029 × 10−14 | 0.2924916343 | 2.881029 × 10−14 |
−10 | 0.9093043357 | 0.9093043357 | 6.816769 × 10−14 | 0.9093043357 | 6.816769 × 10−14 |
−5 | 0.3436158983 | 0.3436158983 | 1.532108 × 10−14 | 0.3436158983 | 1.532108 × 10−14 |
0 | 0.7928167252 | 0.7928167252 | 3.141931 × 10−14 | 0.7928167252 | 3.141931 × 10−14 |
5 | 0.4400466777 | 0.4400466777 | 1.393330 × 10−13 | 0.4400466777 | 1.393330 × 10−13 |
10 | 0.6876241187 | 0.6876241187 | 1.110223 × 10−14 | 0.6876241187 | 1.110223 × 10−14 |
15 | 0.5904802556 | 0.5904802556 | 3.366196 × 10−13 | 0.5904802556 | 3.366196 × 10−13 |