Theory and Modern Applications
Table 5 The comparison of numerical result of \(T(x,t)\) obtained by NIM [35], HPM [44], q-HATM, and the exact solution Equation (32), also the absolute (ABS) errors 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
t | x | HPM [44] | NIM [35] | q-HATM \((T^{(3)})\) | Exact | ABS error (NIM) [35] | ABS error (q-HATM) |
|---|---|---|---|---|---|---|---|
0.2 | 0.0 | 1.50300000 | 1.50300000 | 1.50299910 | 1.50299910 | 8.99676 × 10−07 | 3.23882 × 10−10 |
0.25 | 1.50549536 | 1.50549536 | 1.50549446 | 1.50549446 | 8.95993 × 10−07 | 1.66909 × 10−09 | |
0.50 | 1.50798386 | 1.50798386 | 1.50798297 | 1.50798298 | 8.87678 × 10−07 | 2.99663 × 10−09 | |
0.75 | 1.51046246 | 1.51046246 | 1.51046158 | 1.51046158 | 8.74820 × 10−07 | 4.29258 × 10−09 | |
1 | 1.51292811 | 1.51292812 | 1.51292725 | 1.51292726 | 8.57559 × 10−07 | 5.54361 × 10−09 | |
0.4 | 0.0 | 1.50600000 | 1.50600000 | 1.50599280 | 1.50599281 | 7.18965 × 10−06 | 1.03529 × 10−08 |
0.25 | 1.50848674 | 1.50848674 | 1.50847956 | 1.50847959 | 3.18160 × 10−06 | 6.40562 × 10−08 | |
0.50 | 1.51096292 | 1.51096292 | 1.51095579 | 1.51095585 | 7.07245 × 10−06 | 5.29427 × 10−08 | |
0.75 | 1.51342555 | 1.51342554 | 1.51341851 | 1.51341858 | 6.95939 × 10−06 | 7.35124 × 10−08 | |
1 | 1.51587167 | 1.51587166 | 1.51586476 | 1.51586485 | 6.81151 × 10−06 | 9.33146 × 10−08 | |
0.6 | 0.0 | 1.50900000 | 1.50900000 | 1.50897570 | 1.50897578 | 2.42215 × 10−05 | 7.84747 × 10−08 |
0.25 | 1.51147362 | 1.51147362 | 1.51144938 | 1.51144957 | 2.40502 × 10−05 | 3.75925 × 10−07 | |
0.50 | 1.51393300 | 1.51393300 | 1.51390895 | 1.51390924 | 2.37552 × 10−05 | 2.92990 × 10−07 | |
0.75 | 1.51637524 | 1.51637522 | 1.51635148 | 1.51635188 | 2.33399 × 10−05 | 3.96187 × 10−07 | |
1 | 1.51879747 | 1.51879743 | 1.51877413 | 1.51877462 | 2.28085 × 10−05 | 4.95260 × 10−07 |