Skip to main content

Table 6 The results of \(L_{\infty }\) error norms and the related temporal rate of convergence in Test Problem 5.4 with \(M=8\), \(T_{f}=1\), \(\eta =-1\), 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)

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

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

\(\frac{1}{2}\)

4.9238−3

\(\frac{1}{4}\)

1.2592−3

1.9672

\(\frac{1}{8}\)

3.1642−4

1.9926

\(\frac{1}{16}\)

7.9514−5

1.9925

Δt

LG-RBFs [25]

LSEM [29]

Meshless [24]

τ

dx = 0.1

\(N_{e}=20,p_{e}=5\)

C-order

dx = 0.1

\(\frac{1}{2}\)

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

1.1899−2

5.8541−4

1.1306−2

\(\frac{1}{4}\)

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

6.4885−3

2.4834−4

0.9974

5.6005−3

\(\frac{1}{8}\)

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

3.2224−3

1.1379−4

0.9986

2.7770−3

\(\frac{1}{16}\)

\(\frac{1}{80}\)

1.6079−3

5.4413−5

0.9992

1.3862−3