Theory and Modern Applications
Table 2 Computational error norms and order of convergence for Problem 1 when \(\Delta t=h \)
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 | |
10 | – | – | – | – | 5.3290 × 10−4 | – | 1.5741 × 10−4 | – |
20 | 1.3279 × 10−2 | – | 2.0995 × 10−3 | – | 2.9936 × 10−5 | 4.1539 | 8.2199 × 10−4 | 4.2592 |
40 | 4.4730 × 10−3 | 1.5700 | 8.0009 × 10−4 | 1.3918 | 1.5100 × 10−6 | 4.3092 | 4.5177 × 10−8 | 4.1873 |
80 | 1.5282 × 10−3 | 1.5496 | 3.2081 × 10−5 | 1.3183 | 7.5135 × 10−8 | 4.3289 | 2.7099 × 10−8 | 4.0573 |
160 | 5.2715 × 10−4 | 1.5357 | 9.9469 × 10−5 | 1.6892 | 4.2651 × 10−9 | 4.1388 | 1.6778 × 10−9 | 4.0136 |