Theory and Modern Applications
Table 1 The q-HATM solution for \(Q(x,t)\) and \(S(x,t)\) for the first three approximations in comparison with the exact solution Equation (35) when \(\alpha =1\), \(\hbar =-1\), \(k=r=0.1\), \(\lambda =1.5\), and \(n=1\) for Example 4.2
From: A reliable technique to study nonlinear time-fractional coupled Korteweg–de Vries equations
t | x | \(Q^{(3)}\) | Exact | Absolute error | \(S^{(3)}\) | Exact | Absolute error |
|---|---|---|---|---|---|---|---|
0.1 | −1 | 0.49076638 | 0.49076638 | 1.91609 × 10−11 | 1.49076638 | 1.49076638 | 1.91609 × 10−11 |
−0.5 | 0.49574258 | 0.49574258 | 9.63507 × 10−12 | 1.49574258 | 1.49574258 | 9.63518 × 10−12 | |
0 | 0.50073999 | 0.50073999 | 2.95985 × 10−13 | 1.50073999 | 1.50073999 | 2.95985 × 10−13 | |
0.5 | 0.50573370 | 0.50573370 | 1.02143 × 10−11 | 1.50573370 | 1.50573370 | 1.02145 × 10−11 | |
1 | 0.51069890 | 0.51069890 | 1.97036 × 10−11 | 1.51069890 | 1.51069890 | 1.97036 × 10−11 | |
0.3 | −1 | 0.49223566 | 0.49223566 | 1.50771 × 10−09 | 1.49223566 | 1.49223566 | 1.50771 × 10−09 |
−0.5 | 0.49722072 | 0.49722072 | 7.33337 × 10−10 | 1.49722072 | 1.49722072 | 7.33337 × 10−10 | |
0 | 0.50221964 | 0.50221964 | 7.18815 × 10−11 | 1.50221964 | 1.50221964 | 7.18814 × 10−11 | |
0.5 | 0.50720748 | 0.50720748 | 8.74064 × 10−10 | 1.50720748 | 1.50720748 | 8.74064 × 10−10 | |
1 | 0.51215953 | 0.51215953 | 1.63955 × 10−09 | 1.51215953 | 1.51215953 | 1.63955 × 10−09 | |
0.5 | −1 | 0.49370833 | 0.49370832 | 1.12888 × 10−08 | 1.49370833 | 1.49370832 | 1.12888 × 10−08 |
−0.5 | 0.49870008 | 0.49870007 | 5.29376 × 10−09 | 1.49870008 | 1.49870007 | 5.29376 × 10−09 | |
0 | 0.50369831 | 0.50369831 | 9.24074 × 10−10 | 1.50369831 | 1.50369831 | 9.24074 × 10−10 | |
0.5 | 0.50867811 | 0.50867812 | 7.10289 × 10−09 | 1.50867811 | 1.50867812 | 7.10289 × 10−09 | |
1 | 0.51361491 | 0.51361493 | 1.29837 × 10−08 | 1.51361491 | 1.51361493 | 1.29837 × 10−08 |