Theory and Modern Applications
Table 1 \(\pmb{\|\cdot\|_{2}}\) errors and convergence orders of numerical solution u at \(\pmb{T=5}\) for \(\pmb{p=2,4,\mbox{ and }6}\)
From: A second-order Fourier pseudospectral method for the generalized regularized long wave equation
Δ t | p  = 2 | order | p  = 4 | order | p  = 6 | order |
|---|---|---|---|---|---|---|
0.1 | 2.2055199e−3 | - | 7.4971272e−3 | - | 2.4952949e−2 | - |
0.05 | 5.5175158e−4 | 1.9990 | 1.6977751e−3 | 2.1426 | 4.2548344e−3 | 2.5520 |
0.025 | 1.3823443e−4 | 1.9969 | 4.0822074e−4 | 2.0562 | 9.1684708e−4 | 2.2143 |
0.0125 | 3.4646085e−5 | 1.9963 | 1.0027214e−4 | 2.0254 | 2.1345592e−4 | 2.1027 |
0.00625 | 8.8159403e−6 | 1.9745 | 2.4863890e−5 | 2.0117 | 5.1499083e−5 | 2.0513 |