Theory and Modern Applications
Table 6 The comparison of \(Q^{(3)}\) 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 | 3.29064147 × 10−06 | 6.71934675 × 10−10 | 6.71934619 × 10−10 |
0.4 | 5.25218196 × 10−05 | 1.71161347 × 10−07 | 1.71161347 × 10−07 | |
0.7 | 1.59782942 × 10−04 | 1.59369985 × 10−06 | 1.59369985 × 10−06 | |
1 | 3.22767452 × 10−04 | 6.57484219 × 10−06 | 6.57484219 × 10−06 | |
0.5 | 0.1 | 1.38149650 × 10−06 | 6.58959998 × 10−10 | 6.58959942 × 10−10 |
0.4 | 2.31930879 × 10−05 | 1.67074152 × 10−07 | 1.67074152 × 10−07 | |
0.7 | 7.01626041 × 10−05 | 1.54837628 × 10−06 | 1.54837628 × 10−06 | |
1 | 1.40076591 × 10−04 | 6.35798215 × 10−06 | 6.35798215 × 10−06 | |
0.8 | 0.1 | 9.15781425 × 10−07 | 6.36098785 × 10−10 | 6.36098729 × 10−10 |
0.4 | 6.66717054 × 10−06 | 1.60497911 × 10−07 | 1.60497911 × 10−07 | |
0.7 | 2.02965453 × 10−05 | 1.48018652 × 10−06 | 1.48018652 × 10−06 | |
1 | 4.38927993 × 10−05 | 6.04820333 × 10−06 | 6.04820333 × 10−06 | |
1 | 0.1 | 2.91716151 × 10−06 | 6.15647311 × 10−10 | 6.15647255 × 10−10 |
0.4 | 2.70136817 × 10−05 | 1.54812132 × 10−07 | 1.54812132 × 10−07 | |
0.7 | 8.09801900 × 10−05 | 1.42286375 × 10−06 | 1.42286375 × 10−06 | |
1 | 1.66806976 × 10−04 | 5.79386759 × 10−06 | 5.79386759 × 10−06 |