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Theory and Modern Applications

Table 2 The q-HATM solution for \(Q(x,t)\) and \(S(x,t)\) for the first three approximations in comparison with the exact solution Equation (46) when \(\alpha =1\), \(\hbar =-1\), \(\mathcal{A}=r=0.1\), \(\mathcal{B}=3\), and \(n=1\) for Example 4.3

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

0.78280644

0.78280644

8.60119 × 10−11

0.17504084

0.17504084

1.92328 × 10−11

−0.5

0.93769338

0.93769338

2.24731 × 10−10

0.20967461

0.20967461

5.02514 × 10−11

0

0.99997500

0.99997500

4.16661 × 10−10

0.22360121

0.22360121

9.31682 × 10−11

0.5

0.94229778

0.94229778

2.27333 × 10−10

0.21070419

0.21070419

5.08333 × 10−11

1

0.79007490

0.79007490

8.41223 × 10−11

0.17666612

0.17666612

1.88103 × 10−11

0.3

−1

0.77548344

0.77548343

7.11796 × 10−09

0.17340337

0.17340337

1.59162 × 10−09

−0.5

0.93293648

0.93293649

1.79914 × 10−08

0.20861094

0.20861094

4.02300 × 10−09

0

0.99977500

0.99977503

3.37457 × 10−08

0.22355649

0.22355649

7.54577 × 10−09

0.5

0.94674634

0.94674636

1.86237 × 10−08

0.21169892

0.21169892

4.16438 × 10−09

1

0.79728485

0.79728485

6.65882 × 10−09

0.17827831

0.17827831

1.48896 × 10−09

0.5

−1

0.76810985

0.76810979

5.60719 × 10−08

0.17175458

0.17175457

1.25381 × 10−08

−0.5

0.92803044

0.92803057

1.37181 × 10−07

0.20751391

0.20751394

3.06747 × 10−08

0

0.99937500

0.99937526

2.60324 × 10−07

0.22346704

0.22346710

5.82103 × 10−08

0.5

0.95103569

0.95103584

1.45310 × 10−07

0.21265805

0.21265808

3.24923 × 10−08

1

0.80443236

0.80443231

5.01678 × 10−08

0.17987654

0.17987653

1.12179 × 10−08