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Theory and Modern Applications

Table 4 The comparison of the exact solution with HPTM solution of \({\psi }({{\chi }},{{\eta }})\) at \({\eta }=0.01\)

From: Numerical investigation of fractional-order Kersten–Krasil’shchik coupled KdV–mKdV system with Atangana–Baleanu derivative

χ

Exact result

HPTM result

Absolute error

5

−0.00003128920578

−0.00005018707030

1.889786452E−09

4

−0.00002953283553

−0.00003941505303

9.882217500E−09

3

−0.00002464651012

−0.00002354262325

1.103886870E−08

2

−0.00001563187126

−0.00001368571425

1.946157010E−08

1

−0.000009064576442

−0.000008133706541

9.3086990E−08

0

−1.060578884000000

−1.050550263000000

1.769181166E−07

−1

−0.000008032738383

−0.000008064752114

3.080452365E−08

−2

−0.00001648493229

−0.00001351283541

2.711411868E−08

−3

−0.00002345262104

−0.00002565550250

1.387225658E−08

−4

−0.00002833704423

−0.00002832282225

5.778090290E−09

−5

−0.00003218607047

−0.00003218920551

2.226059143E−09