Theory and Modern Applications
Table 9 The comparison of numerical result of \(Q(x,t)\) obtained by NIM [43], q-HATM, and the exact solution Equation (35), also the absolute (ABS) errors when \(\alpha =1\), \(\hbar =-1\), \(k=r=\lambda =0.1\), and \(n=1\) for Example 4.2
From: A reliable technique to study nonlinear time-fractional coupled Korteweg–de Vries equations
x | NIM [43] | q-HATM \((Q^{(3)})\) | Exact | ABS error (NIM) [43] | ABS error (q-HATM) |
|---|---|---|---|---|---|
−50 | 0.400010 | 0.400010 | 0.400010 | 2.48113 × 10−08 | 1.15064 × 10−11 |
−40 | 0.400072 | 0.400072 | 0.400072 | 1.83213 × 10−07 | 8.46214 × 10−11 |
−30 | 0.400531 | 0.400532 | 0.400532 | 1.34729 × 10−06 | 6.03700 × 10−10 |
−20 | 0.403859 | 0.403868 | 0.403868 | 9.60358 × 10−06 | 3.38628 × 10−09 |
−10 | 0.425385 | 0.425439 | 0.425439 | 5.33734 × 10−05 | 5.51964 × 10−09 |
0 | 0.503672 | 0.503698 | 0.503698 | 2.60625 × 10−05 | 9.24074 × 10−10 |
10 | 0.577740 | 0.577670 | 0.577670 | 6.95746 × 10−05 | 4.87746 × 10−09 |
20 | 0.596671 | 0.596655 | 0.596655 | 1.61881 × 10−05 | 3.31997 × 10−09 |
30 | 0.599543 | 0.599541 | 0.599541 | 2.36055 × 10−06 | 5.86792 × 10−10 |
40 | 0.599938 | 0.599938 | 0.599938 | 3.22719 × 10−07 | 8.21664 × 10−11 |
50 | 0.599992 | 0.599992 | 0.599992 | 4.37352 × 10−08 | 1.11710 × 10−11 |