Table 1 Maximum point wise error \(\tilde{E}_\varepsilon ^{N_z,N_t}\), uniform error \(\tilde{E}^{N_z,N_t}\),convergence rate \(\tilde{R}^{N_z,N_t}\), and CPU time in second for Example 1, \(N=M\)
\(\varepsilon \downarrow \) | \(N = 16\) | \(N = 32\) | \(N = 64\) | \(N = 128\) | \(N = 256\) | \(N = 512\) |
|---|---|---|---|---|---|---|
\(2^{-0}\) | 4.5471e-04 | 2.4759e-04 | 1.2990e-04 | 6.6937e-05 | 3.3972e-05 | 1.7125e-05 |
\(2^{-4}\) | 2.2371e-03 | 1.2671e-03 | 6.8474e-04 | 3.5796e-04 | 1.8316e-04 | 9.2701e-05 |
\(2^{-12}\) | 5.9805e-03 | 3.6088e-03 | 1.9579e-03 | 1.0167e-03 | 5.1748e-04 | 2.5419e-04 |
\(2^{-16}\) | 5.9805e-03 | 3.6088e-03 | 1.9579e-03 | 1.0167e-03 | 5.1773e-04 | 2.6120e-04 |
\(2^{-20}\) | 5.9805e-03 | 3.6088e-03 | 1.9579e-03 | 1.0167e-03 | 5.1773e-04 | 2.6120e-04 |
\(2^{-24}\) | 5.9805e-03 | 3.6088e-03 | 1.9579e-03 | 1.0167e-03 | 5.1773e-04 | 2.6120e-04 |
\(2^{-28}\) | 5.9805e-03 | 3.6088e-03 | 1.9579e-03 | 1.0167e-03 | 5.1773e-04 | 2.6120e-04 |
\(\tilde{E}^{N_z,N_t}\) | 5.9805e-03 | 3.6088e-03 | 1.9579e-03 | 1.0167e-03 | 5.1773e-04 | 2.6120e-04 |
\(\tilde{R}^{N_z,N_t}\) | 7.2877e-01 | 8.8219e-01 | 9.4545e-01 | 9.7359e-01 | 9.8703e-01 | – |
CPU time (s) | 0.0536 | 0.0659 | 0.0897 | 0.1120 | 0.4506 | 2.7989 |