Theory and Modern Applications
Table 7 The comparison of \(S^{(3)}\) solution obtained by DTM, RDTM [40], and q-HATM with the exact solution Equation (32) in terms of absolute error when \(\alpha =1\), \(\hbar =-1\), \(k=\eta =0.1\), \(p=1.5\), \(r=-1.5\), and \(n=1\) for Example 4.1
From: A reliable technique to study nonlinear time-fractional coupled Korteweg–de Vries equations
x | t | DTM [40] | RDTM [40] | q-HATM |
|---|---|---|---|---|
0.2 | 0.1 | 5.63621150 × 10−10 | 1.56042290 × 10−10 | 1.56042734 × 10−10 |
0.4 | 5.68117962 × 10−08 | 5.54534330 × 10−08 | 5.54534325 × 10−08 | |
0.7 | 6.66098903 × 10−07 | 6.63837052 × 10−07 | 6.63837052 × 10−07 | |
1 | 3.35673755 × 10−06 | 3.35365276 × 10−06 | 3.35365276 × 10−06 | |
0.5 | 0.1 | 2.12791820 × 10−08 | 3.57261776 × 10−10 | 3.57261776 × 10−10 |
0.4 | 1.64465393 × 10−07 | 1.06591274 × 10−07 | 1.06591274 × 10−07 | |
0.7 | 1.23169306 × 10−06 | 1.13888355 × 10−06 | 1.13888355 × 10−06 | |
1 | 5.43336084 × 10−06 | 5.30892913 × 10−06 | 5.30892913 × 10−06 | |
0.8 | 0.1 | 1.70237973 × 10−07 | 5.53058488 × 10−10 | 5.53058932 × 10−10 |
0.4 | 5.66500685 × 10−07 | 1.56115444 × 10−07 | 1.56115444 × 10−07 | |
0.7 | 2.23353809 × 10−06 | 1.59675253 × 10−06 | 1.59675253 × 10−06 | |
1 | 8.02493433 × 10−06 | 7.18451241 × 10−06 | 7.18451242 × 10−06 | |
1 | 0.1 | 4.67602796 × 10−07 | 6.79135415 × 10−10 | 6.79134970 × 10−10 |
0.4 | 1.23973634 × 10−06 | 1.87873466 × 10−07 | 1.87873466 × 10−07 | |
0.7 | 3.48931405 × 10−06 | 1.88914547 × 10−06 | 1.88914547 × 10−06 | |
1 | 1.04684751 × 10−05 | 8.37722635 × 10−06 | 8.37722635 × 10−06 |