Theory and Modern Applications
Table 4 \(L^{\infty }\)-norm errors and convergence orders of Ṽ obtained by the fourth-order scheme for Example 2
τ | h | α = 1.2 | α = 1.5 | α = 1.8 | α = 2.0 | ||||
|---|---|---|---|---|---|---|---|---|---|
\( \Vert v^{n}-\widetilde{V}^{n} \Vert _{\infty }\) | Order | \(\Vert v^{n}-\widetilde{V}^{n} \Vert _{\infty }\) | Order | \(\Vert v^{n}-\widetilde{V}^{n} \Vert _{\infty }\) | Order | \(\Vert v^{n}-\widetilde{V}^{n} \Vert _{\infty }\) | Order | ||
1/8 | 1/8 | 4.91e−02 | 1.55 | 2.13e−02 | 2.45 | 2.62e−02 | 2.41 | 2.14e−02 | 2.86 |
1/16 | 1/16 | 7.69e−03 | 2.67 | 3.27e−03 | 2.71 | 2.14e−03 | 3.62 | 1.41e−03 | 3.93 |
1/32 | 1/32 | 7.16e−04 | 3.43 | 2.83e−04 | 3.53 | 1.40e−04 | 3.93 | 9.17e−05 | 3.94 |
1/64 | 1/64 | 5.15e−05 | 3.80 | 1.92e−05 | 3.88 | 8.98e−06 | 3.97 | 5.92e−06 | 3.95 |