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Table 9 The results of \(\mathcal{E}_{2}/\mathcal{E}_{\infty }\) error norms and the related spatial rate of convergence in Test Problem 5.4 with \(\Delta t=0.001\), \(T_{f}=1\), \(\eta =\pm 1\), and diverse M on \([-1,1]\)

From: Time accurate solution to Benjamin–Bona–Mahony–Burgers equation via Taylor–Boubaker series scheme

M

η = −1

\(\mathcal{E}_{2}\)

ROCx2

\(\mathcal{E}_{\infty }\)

\(\operatorname{ROCx}_{\infty }\)

2

3.8426−2

8.6267−2

4

2.8716−3

3.7421

8.3279−3

3.3728

8

6.4843−5

5.4688

3.1262−4

4.7355

16

2.8165−8

11.169

1.3819−7

11.144

M

η = +1

\(\mathcal{E}_{2}\)

ROCx2

\(\mathcal{E}_{\infty }\)

\(\operatorname{ROCx}_{\infty }\)

2

1.9233−2

5.0755−2

4

9.1990−4

4.3860

3.8484−3

3.7212

8

7.8660−5

3.5478

3.4115−4

3.4958

16

1.9247−8

11.997

8.8667−8

11.910