Theory and Modern Applications
Table 4 The comparative study of \(\operatorname{Im}{[\mathcal {W}_{(3)}]}\) 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 | 0.0079063274 | 0.0079063274 | 1.225582 × 10−14 | 0.0079063274 | 1.225582 × 10−14 |
−10 | −0.0020455489 | −0.0020455489 | 1.109139 × 10−14 | −0.0020455489 | 1.109139 × 10−14 |
−5 | −0.0410293761 | −0.0410293761 | 1.890016 × 10−13 | −0.0410293761 | 1.890016 × 10−13 |
0 | −0.0649954753 | −0.0649954753 | 3.137629 × 10−13 | −0.0649954753 | 3.137629 × 10−13 |
5 | −0.0193551372 | −0.0193551372 | 1.423792 × 10−13 | −0.0193551372 | 1.423792 × 10−13 |
10 | 0.0046715148 | 0.0046715148 | 1.504092 × 10−14 | 0.0046715148 | 1.504092 × 10−14 |
15 | 0.0084703527 | 0.0084703527 | 7.089815 × 10−15 | 0.0084703527 | 7.089815 × 10−15 |