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Theory and Modern Applications

Table 8 The comparison of \(T^{(3)}\) solution obtained by DTM, RDTM [40], and q-HATM with the exact solution Equation (32) in terms of absolute error 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

x

t

DTM [40]

RDTM [40]

q-HATM

0.2

0.1

2.79944734 × 10−10

7.75046693 × 10−11

7.75046693 × 10−11

0.4

2.82177797 × 10−08

2.75430956 × 10−08

2.75430956 × 10−08

0.7

3.30843826 × 10−07

3.29720390 × 10−07

3.29720390 × 10−07

1

1.66725375 × 10−06

1.66572157 × 10−06

1.66572157 × 10−06

0.5

0.1

1.05691302 × 10−08

1.77448056 × 10−10

1.77448056 × 10−10

0.4

8.16881098 × 10−08

5.29426858 × 10−08

5.29426858 × 10−08

0.7

6.11768076 × 10−07

5.65670636 × 10−07

5.65670636 × 10−07

1

2.69868916 × 10−06

2.63688533 × 10−06

2.63688533 × 10−06

0.8

0.1

8.45552843 × 10−08

2.74697820 × 10−10

2.74697820 × 10−10

0.4

2.81374512 × 10−07

7.75407836 × 10−08

7.75407836 × 10−08

0.7

1.10937322 × 10−06

7.93089006 × 10−07

7.93089006 × 10−07

1

3.98589453 × 10−06

3.56846643 × 10−06

3.56846643 × 10−06

1

0.1

2.32253045 × 10−07

3.37318617 × 10−10

3.37318617 × 10−10

0.4

6.15763083 × 10−07

9.33146349 × 10−08

9.33146349 × 10−08

0.7

1.73310301 × 10−06

9.38317285 × 10−07

9.38317285 × 10−07

1

5.19957370 × 10−06

4.16087401 × 10−06

4.16087401 × 10−06