Theory and Modern Applications
Table 1 Maximum errors and spatial convergence orders of difference scheme (2.14)–(2.16) for Example 5.1 with \(\alpha = 0.5\); \(\sigma = 0.1\); \(T = 1.5\); \(N = 800\)
M | β = 1.3 | β = 1.5 | β = 1.8 | |||
|---|---|---|---|---|---|---|
e(h,τ,σ) | \(\mathit{rate}_{h}\) | e(h,τ,σ) | \(\mathit{rate}_{h}\) | e(h,τ,σ) | \(\mathit{rate}_{h}\) | |
20 | 3.978980e−03 | – | 1.594856e−03 | – | 9.815094e−04 | – |
40 | 2.181749e−03 | 0.8669 | 8.201275e−04 | 0.9595 | 3.974269e−04 | 1.3043 |
80 | 1.144519e−03 | 0.9307 | 4.133978e−04 | 0.9883 | 1.779229e−04 | 1.1594 |
160 | 5.855271e−04 | 0.9669 | 2.080332e−04 | 0.9907 | 8.429100e−05 | 1.0778 |
320 | 2.950680e−04 | 0.9887 | 1.046050e−04 | 0.9919 | 4.121610e−05 | 1.0322 |