Theory and Modern Applications
Table 5 Absolute errors for \(N=3\) and \(\mathfrak{h}(t)=\cos (t)\) 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 × 10−20 | 1.00 × 10−21 | 1.00 × 10−21 | 2.00 × 10−21 | 0.00 |
(0.2, 0.2) | 4.00 × 10−20 | 0.00 | 1.00 × 10−20 | 2.00 × 10−20 | 0.00 |
(0.3, 0.3) | 1.60 × 10−19 | 1.00 × 10−20 | 6.00 × 10−20 | 5.00 × 10−20 | 4.00 × 10−20 |
(0.4, 0.4) | 3.00 × 10−19 | 3.00 × 10−20 | 9.00 × 10−20 | 9.00 × 10−20 | 4.00 × 10−20 |
(0.5, 0.5) | 6.00 × 10−19 | 2.00 × 10−20 | 1.40 × 10−19 | 2.30 × 10−19 | 0.00 |
(0.6, 0.6) | 1.00 × 10−18 | 0.00 | 1.00 × 10−19 | 3.20 × 10−19 | 1.00 × 10−19 |
(0.7, 0.7) | 1.61 × 10−18 | 9.00 × 10−20 | 0.00 | 4.70 × 10−19 | 1.90 × 10−19 |
(0.8, 0.8) | 2.47 × 10−18 | 6.70 × 10−19 | 7.10 × 10−19 | 1.37 × 10−18 | 3.10 × 10−19 |
(0.9, 0.9) | 3.56 × 10−18 | 1.95 × 10−18 | 1.41 × 10−18 | 2.38 × 10−18 | 1.69 × 10−18 |
(1.0, 1.0) | 6.03 × 10−18 | 7.10 × 10−18 | 6.06 × 10−18 | 7.60 × 10−18 | 5.54 × 10−18 |