Theory and Modern Applications
Table 2 The comparative study of \(\operatorname{Im}{[\mathcal {W}_{(3)}]}\) solutions of δ-HPTM, q-HATM, and exact solution for Example 1 at \(\beta_{1}=1, \beta_{2}=2, \beta_{3}=0.1, y=2, z=2, \xi=0.1, e_{0}=3, p=0.5, q=0.5, \phi=1\), and \(t=0.01\)
x | Exact | δ-HPTM (δ = 1) | q-HPTM (n = 1,ħ = 1) | ||
|---|---|---|---|---|---|
Approx | Absolute error | Approx | Absolute error | ||
−15 | 0.0014301059 | 0.0014301059 | 1.789911 × 10−12 | 0.0014301059 | 1.789911 × 10−12 |
−10 | −0.0084303978 | −0.0084303979 | 2.285488 × 10−11 | −0.0084303979 | 2.285488 × 10−11 |
−5 | −0.0100504513 | −0.0100504513 | 6.996747 × 10−11 | −0.0100504513 | 6.996747 × 10−11 |
0 | 0.0168457860 | 0.0168457860 | 6.948674 × 10−12 | 0.0168457860 | 6.948674 × 10−12 |
5 | 0.0002672659 | 0.0002672659 | 4.853362 × 10−13 | 0.0002672659 | 4.853362 × 10−13 |
10 | −0.0015748494 | −0.0015748494 | 7.746273 × 10−13 | −0.0015748494 | 7.746273 × 10−13 |
15 | −0.0008303837 | −0.0008303837 | 5.348478 × 10−14 | −0.0008303837 | 5.348478 × 10−14 |