Theory and Modern Applications
Table 4 Computational error norms and order of convergence for Problem 2 when \(\gamma =0.5\)
n | Method in [21] | Proposed method | ||||||
|---|---|---|---|---|---|---|---|---|
Δt = 0.000001, t = 0.0001 | Δt = 0.01, t = 1 | |||||||
\(L_{\infty }\) | χ | \(L_{2}\) | χ | \(L_{\infty }\) | χ | \(L_{2}\) | χ | |
20 | 1.0861 × 10−2 | – | 1.7173 × 10−3 | – | 9.5789 × 10−4 | – | 9.4891 × 10−4 | – |
40 | 3.9014 × 10−3 | 1.4771 | 5.3619 × 10−4 | 1.6793 | 4.9968 × 10−5 | 4.2606 | 4.8987 × 10−5 | 4.2763 |
80 | 1.3892 × 10−3 | 1.4897 | 2.0983 × 10−4 | 1.3535 | 2.4519 × 10−6 | 4.3490 | 2.4361 × 10−6 | 4.3291 |
160 | 4.9276 × 10−4 | 1.4953 | 6.7546 × 10−5 | 1.6353 | 1.2826 × 10−7 | 4.2567 | 1.2943 × 10−7 | 4.2578 |