Table 2 The results of \(L_{\infty }\) error norms, CPU times, and the related temporal rate of convergence in Test Problem 5.1 with \(M=10\) and diverse Δt
From: Time accurate solution to Benjamin–Bona–Mahony–Burgers equation via Taylor–Boubaker series scheme
Δt | Taylor–Boubaker (M = 10) | FODM [7] (h = 10−3) | ||||
|---|---|---|---|---|---|---|
\(\mathcal{E}_{\infty }\) | \(\operatorname{ROCt}_{\infty }\) | CPU(s) | k | \(e_{\infty }(h,k)\) | \(\operatorname{Order}_{k}\) | |
\(\frac{1}{2}\) | 8.620986 × 10−3 | – | 0.47193 | \(\frac{1}{10}\) | 3.117640 × 10−4 | – |
\(\frac{1}{4}\) | 2.119906 × 10−3 | 2.0239 | 0.94799 | \(\frac{1}{20}\) | 7.787890 × 10−5 | 2.001150 |
\(\frac{1}{8}\) | 5.286064 × 10−4 | 2.0037 | 1.89863 | \(\frac{1}{40}\) | 1.946593 × 10−5 | 2.000280 |
\(\frac{1}{16}\) | 1.328693 × 10−4 | 1.9922 | 3.80004 | \(\frac{1}{80}\) | 4.866066 × 10−6 | 2.000123 |