Theory and Modern Applications
Table 4 Comparative study between ADM [28], VIM [29], LADM [30], CRFDTM [26] and q-HATM for the approximate solution \(v(x,t)\) at \(\omega =0.005\), \(\ell= 0.1\), \(c=10\), \(\alpha =1 \) and \(\hslash =-1\) for Example 6.2
From: A reliable technique for fractional modified Boussinesq and approximate long wave equations
(x,t) | \(\vert {v}_{\mathrm{Exact}} - {v}_{\mathrm{ADM}} \vert \) | \(\vert {v}_{\mathrm{Exact}} - {v}_{\mathrm{VIM}} \vert \) | \(\vert {v}_{\mathrm{Exact}} - {v}_{\mathrm{LADM}} \vert \) | \(\vert {v}_{\mathrm{Exact}} - {v}_{\mathrm{CRFDTM}} \vert \) | \(\vert {v}_{\mathrm{Exact}} - {v}_{{q}\text{-}\mathrm{HATM}}^{ ( {3} )} \vert \) |
|---|---|---|---|---|---|
(0.1,0.1) | 4.81902 × 10−4 | 1.23033 × 10−4 | 9.5512 × 10−10 | 1.73472 × 10−18 | 1.73472 × 10−18 |
(0.1,0.3) | 4.50818 × 10−4 | 1.7600 × 10−4 | 8.0600 × 10−10 | 2.60209 × 10−17 | 2.60209 × 10−17 |
(0.1,0.5) | 4.22221 × 10−4 | 2.69597 × 10−4 | 6.7700 × 10−10 | 1.80411 × 10−16 | 1.80411 × 10−16 |
(0.2,0.1) | 9.76644 × 10−4 | 2.69597 × 10−4 | 3.8210 × 10−9 | 3.46945 × 10−18 | 3.46945 × 10−18 |
(0.2,0.3) | 9.13502 × 10−4 | 2.69597 × 10−4 | 3.224 × 10−9 | 2.34188 × 10−17 | 2.34188 × 10−17 |
(0.2,0.5) | 8.55426 × 10−4 | 2.69597 × 10−4 | 2.7060 × 10−9 | 1.73472 × 10−16 | 1.73472 × 10−16 |
(0.3,0.1) | 1.48482 × 10−3 | 2.69597 × 10−4 | 8.597 × 10−9 | 3.46945 × 10−18 | 3.46945 × 10−18 |
(0.3,0.3) | 1.38858 × 10−3 | 2.69597 × 10−4 | 7.252 × 10−9 | 1.99493 × 10−17 | 1.99493 × 10−17 |
(0.3,0.5) | 1.30009 × 10−3 | 2.69597 × 10−4 | 6.0910 × 10−9 | 1.61329 × 10−16 | 1.61329 × 10−16 |
(0.4,0.1) | 2.00705 × 10−3 | 2.69597 × 10−4 | 1.5284 × 10−8 | 2.60209 × 10−18 | 2.60209 × 10−18 |
(0.4,0.3) | 1.87661 × 10−3 | 2.69597 × 10−4 | 1.2893 × 10−8 | 1.73472 × 10−17 | 1.73472 × 10−17 |
(0.4,0.5) | 1.75670 × 10−3 | 2.69597 × 10−4 | 1.0827 × 10−8 | 1.52656 × 10−16 | 1.52656 × 10−16 |
(0.5,0.1) | 2.54396 × 10−3 | 2.69597 × 10−4 | 2.3880 × 10−8 | 8.67362 × 10−19 | 8.67362 × 10−19 |
(0.5,0.3) | 2.37815 × 10−3 | 2.69597 × 10−4 | 2.0144 × 10−8 | 2.08167 × 10−17 | 2.08167 × 10−17 |
(0.5,0.5) | 2.22578 × 10−3 | 2.69597 × 10−4 | 1.6916 × 10−8 | 1.43982 × 10−16 | 1.43982 × 10−16 |