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Boundary Value Problems

Table 7 The results of \(L_{\infty }\) error norms and the related temporal rate of convergence in Test Problem 5.4 with \(M=8\), \(T_{f}=0.1\), \(\eta =+1\), and diverse Δt on \([0,1]\)

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

Δt

TBM (M = 8)

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

ROCt2

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

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

\(\frac{1}{10}\)

1.5275−6

–

8.8717−5

–

\(\frac{1}{20}\)

2.5300−7

2.5939

2.1601−5

2.0381

\(\frac{1}{40}\)

8.8279−8

1.5190

4.9149−6

2.1359

Δt

ICSCM [23]

Meshless [24]

\(L_{2}\)

\(L_{\infty }\)

\(L_{2}\)

\(L_{\infty }\)

\(\frac{1}{10}\)

3.1380−4

5.2316−4

4.8125−3

2.4109−3

\(\frac{1}{20}\)

1.6563−4

2.7764−4

2.3406−3

1.1911−3

\(\frac{1}{40}\)

8.5147−5

1.4284−4

1.1793−3

6.0771−4

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