Theory and Modern Applications
Table 1 The comparative study of \(\operatorname{Re}{[\mathcal {W}_{(3)}]}\) 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 | 3.0037055813 | 3.0037055813 | 2.007727 × 10−12 | 3.0037055813 | 2.007727 × 10−12 |
−10 | 3.00796331114 | 3.0079633111 | 1.639577 × 10−12 | 3.0079633111 | 1.639577 × 10−12 |
−5 | 2.9790685680 | 2.9790685680 | 5.847900 × 10−11 | 2.9790685680 | 5.847900 × 10−11 |
0 | 3.0010839974 | 3.0010839974 | 4.721068 × 10−11 | 3.0010839974 | 4.721068 × 10−11 |
5 | 3.0062055680 | 3.0062055680 | 6.424195 × 10−12 | 3.0062055680 | 6.424195 × 10−12 |
10 | 3.0014721223 | 3.0014721223 | 5.728751 × 10−14 | 3.0014721223 | 5.728751 × 10−14 |
15 | 3.0001939705 | 3.0001939705 | 1.092459 × 10−13 | 3.0001939705 | 1.092459 × 10−13 |