Theory and Modern Applications
Table 4 The comparison of numerical result of \(S(x,t)\) 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 (\(S^{(3)}\)) | Exact | ABS error (NIM) [35] | ABS error (q-HATM) |
|---|---|---|---|---|---|---|---|
0.2 | 0.0 | −3.0139600 | −3.0139600 | −3.01396181 | −3.01396181 | 1.81135 × 10−06 | 6.52082 × 10−10 |
0.25 | −3.0089360 | −3.0089360 | −3.00893782 | −3.00893782 | 1.80393 × 10−06 | 3.36043 × 10−09 | |
0.50 | −3.0039258 | −3.0039258 | −3.00392761 | −3.00392761 | 1.78719 × 10−06 | 6.03321 × 10−09 | |
0.75 | −2.9989356 | −2.9989356 | −2.99893736 | −2.99893735 | 1.76130 × 10−06 | 8.64240 × 10−09 | |
1 | −2.9939714 | −2.9939714 | −2.99397313 | −2.99397312 | 1.72655 × 10−06 | 1.11611 × 10−08 | |
0.4 | 0.0 | −3.0079200 | −3.0079200 | −3.00793450 | −3.00793448 | 1.44752 × 10−05 | 2.08439 × 10−08 |
0.25 | −3.0029134 | −3.0029133 | −3.00292783 | −3.00292776 | 1.43943 × 10−05 | 6.40562 × 10−08 | |
0.50 | −2.9979279 | −2.9979279 | −2.99794233 | −2.99794223 | 1.42392 × 10−05 | 1.06591 × 10−07 | |
0.75 | −2.9929699 | −2.9929699 | −2.99298407 | −2.99298392 | 1.40116 × 10−05 | 1.48005 × 10−07 | |
1 | −2.9880450 | −2.9880450 | −2.98805896 | −2.98805877 | 1.37138 × 10−05 | 1.87873 × 10−07 | |
0.6 | 0.0 | −3.0018800 | −3.0018800 | −3.00192892 | −3.00192877 | 4.87660 × 10−05 | 1.57996 × 10−07 |
0.25 | −2.9968998 | −2.9968997 | −2.99694857 | −2.99694820 | 4.84210 × 10−05 | 3.75925 × 10−07 | |
0.50 | −2.9919482 | −2.9919482 | −2.99199664 | −2.99199605 | 4.78272 × 10−05 | 5.89887 × 10−07 | |
0.75 | −2.9870312 | −2.9870312 | −2.98707902 | −2.98707822 | 4.69909 × 10−05 | 7.97657 × 10−07 | |
1 | −2.9821544 | −2.9821545 | −2.98220143 | −2.98220043 | 4.59211 × 10−05 | 9.97124 × 10−07 |