Theory and Modern Applications
Table 7 Errors and convergence orders of scheme (62)–(64) with an optimal step size ratio for τ, \(h_{1}\), \(h_{2}\), \(h_{3}\) and Δβ (Example 2)
τ | \(h_{1}=h_{2}\) | Δβ | \(\|e^{N} \|_{L^{2}}\) | Order | \(\|e^{N} \|_{L^{\infty}}\) | Order | CPU time |
|---|---|---|---|---|---|---|---|
1/16 | π/4 | 1/2 | 0.1708 | – | 0.0992 | – | 0.0033 s |
1/256 | π/16 | 1/4 | 0.0107 | 3.9966 | 0.0063 | 3.9769 | 0.2109 s |
1/4096 | π/64 | 1/8 | 6.5768e−04 | 4.0241 | 3.8735e−04 | 4.0236 | 1 h 6 m 37 s |