Theory and Modern Applications
Table 4 Absolute errors for \(N=3\) and \(\mathfrak{h}(t)=t\) at equally spaced points \((x_{j}, t_{j})\) for Example 6.3
\((x_{j}, t_{j})\) | \(\sigma (x, t)=1-0.5 e^{-xt}\) | \(\sigma (x, t)=1-\cos (x) e^{-t}\) | σ(x,t)=0.25 | σ(x,t)=0.50 | σ(x,t)=1 |
|---|---|---|---|---|---|
(0.0, 0.0) | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
(0.1, 0.1) | 1.00 × 10−21 | 0.00 | 1.00 × 10−21 | 0.00 | 1.00 × 10−21 |
(0.2, 0.2) | 0.00 | 0.00 | 1.00 × 10−20 | 0.00 | 0.00 |
(0.3, 0.3) | 0.00 | 0.00 | 2.00 × 10−20 | 2.00 × 10−20 | 2.00 × 10−20 |
(0.4, 0.4) | 2.00 × 10−20 | 3.00 × 10−20 | 7.00 × 10−20 | 4.00 × 10−20 | 5.00 × 10−20 |
(0.5, 0.5) | 1.00 × 10−20 | 6.00 × 10−20 | 1.70 × 10−19 | 1.70 × 10−19 | 1.00 × 10−20 |
(0.6, 0.6) | 1.30 × 10−19 | 5.00 × 10−20 | 2.10 × 10−19 | 2.00 × 10−19 | 1.00 × 10−19 |
(0.7, 0.7) | 2.30 × 10−19 | 9.00 × 10−20 | 3.90 × 10−19 | 3.50 × 10−19 | 0.00 |
(0.8, 0.8) | 3.00 × 10−19 | 3.00 × 10−19 | 6.70 × 10−19 | 2.00 × 10−20 | 9.30 × 10−19 |
(0.9, 0.9) | 1.99 × 10−18 | 2.30 × 10−19 | 1.16 × 10−18 | 4.80 × 10−19 | 1.60 × 10−18 |
(1.0, 1.0) | 6.79 × 10−18 | 1.00 × 10−18 | 5.63 × 10−19 | 1.32 × 10−18 | 3.37 × 10−18 |