Table 1 The results of \(L_{\infty }\) error norms, CPU times, and the related spatial rate of convergence in Test Problem 5.1 with \(\Delta t=0.01\) and diverse M
From: Time accurate solution to Benjamin–Bona–Mahony–Burgers equation via Taylor–Boubaker series scheme
M | Taylor–Boubaker (Δt = 10−2) | FODM [7] (k = 10−4) | ||||
|---|---|---|---|---|---|---|
\(\mathcal{E}_{\infty }\) | \(\operatorname{ROCx}_{\infty }\) | CPU(s) | h | \(e_{\infty }(h,k)\) | \(\operatorname{Order}_{h}\) | |
2 | 5.788417 × 10−1 | – | 16.8013 | \(\frac{1}{10}\) | 4.612813 × 10−4 | – |
4 | 9.243067 × 10−2 | 2.6467 | 20.1999 | \(\frac{1}{20}\) | 3.103213 × 10−5 | 3.893812 |
8 | 2.426774 × 10−4 | 8.5732 | 27.4852 | \(\frac{1}{40}\) | 1.980428 × 10−6 | 3.969878 |
16 | 3.371226 × 10−6 | 6.1696 | 45.2692 | \(\frac{1}{80}\) | 1.244767 × 10−7 | 3.991864 |