Theory and Modern Applications
Table 3 The numerical convergence orders in temporal direction with \(\pmb{h=\frac{1}{3{,}000}}\)
τ | α = 0.1 | α = 0.5 | α = 0.9 | |||
|---|---|---|---|---|---|---|
\(\boldsymbol{E_{\infty}(h,\tau)}\) | Order( τ ) | \(\boldsymbol{E_{\infty}(h,\tau)}\) | Order( τ ) | \(\boldsymbol{E_{\infty}(h,\tau)}\) | Order( τ ) | |
1/4 | 8.2922e−003 | * | 4.4237e−002 | * | 7.7457e−002 | * |
1/8 | 2.1607e−003 | 1.9403 | 1.1423e−002 | 1.9533 | 1.9665e−002 | 1.9778 |
1/16 | 5.5117e−004 | 1.9709 | 2.8960e−003 | 1.9798 | 4.9383e−003 | 1.9935 |
1/32 | 1.3948e−004 | 1.9824 | 7.2848e−004 | 1.9911 | 1.2356e−003 | 1.9988 |