Theory and Modern Applications
Table 2 Maximum errors and temporal convergence orders of difference scheme (2.14)–(2.16) for Example 5.1 with \(\alpha = 0.5\); \(\sigma = 0.2\); \(T = 1.5\); \(M = 2000\)
N | β = 1.3 | β = 1.5 | β = 1.8 | |||
|---|---|---|---|---|---|---|
e(h,τ,σ) | \(\mathit{rate}_{\tau}\) | e(h,τ,σ) | \(\mathit{rate}_{\tau}\) | e(h,τ,σ) | \(\mathit{rate}_{\tau}\) | |
5 | 6.897311e−04 | – | 4.256675e−04 | – | 2.559967e−04 | – |
10 | 2.640520e−04 | 1.3852 | 1.711099e−04 | 1.3148 | 1.099115e−04 | 1.2198 |
20 | 8.702462e−05 | 1.6013 | 6.546150e−05 | 1.3862 | 4.935518e−05 | 1.1551 |
40 | 4.570569e−05 | 0.9290 | 3.003826e−05 | 1.1238 | 2.399388e−05 | 1.0405 |