Skip to main content

Theory and Modern Applications

Table 10 The comparison of numerical result of \(S(x,t)\) 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 \((S^{(3)})\)

Exact

ABS error (NIM) [43]

ABS error (q-HATM)

−50

9.77629 × 10−06

9.77690 × 10−06

9.77691 × 10−06

6.24540 × 10−10

1.15064 × 10−11

−40

7.22150 × 10−05

7.22195 × 10−05

7.22196 × 10−05

4.60471 × 10−09

8.46214 × 10−11

−30

5.32373 × 10−04

5.32406 × 10−04

5.32406 × 10−04

3.34797 × 10−08

6.03701 × 10−10

−20

3.86797 × 10−03

3.86819 × 10−03

3.86819 × 10−03

2.19196 × 10−07

3.38628 × 10−09

−10

2.54382 × 10−02

2.54388 × 10−02

2.54388 × 10−02

5.70005 × 10−07

5.51964 × 10−09

0

1.03700 × 10−01

1.03698 × 10−01

1.03698 × 10−01

1.75596 × 10−06

9.24074 × 10−10

10

1.77670 × 10−01

1.77670 × 10−01

1.77670 × 10−01

5.80831 × 10−07

4.87746 × 10−09

20

1.96655 × 10−01

1.96655 × 10−01

1.96655 × 10−01

2.12492 × 10−07

3.31998 × 10−09

30

1.99541 × 10−01

1.99541 × 10−01

1.99541 × 10−01

3.22892 × 10−08

5.86792 × 10−10

40

1.99938 × 10−01

1.99938 × 10−01

1.99938 × 10−01

4.43792 × 10−09

8.21664 × 10−11

50

1.99992 × 10−01

1.99992 × 10−01

1.99992 × 10−01

6.01862 × 10−10

1.11710 × 10−11