Theory and Modern Applications
Table 4 Error norms for Problem 2 at \(t=1\) with \(N=80\), \(\alpha =1.50\)
Δt | Method in [1] | Proposed method | ||
|---|---|---|---|---|
\(L_{\infty }\) | \(L_{2}\) | \(L_{\infty }\) | \(L_{2}\) | |
0.001 | 1.8221 × 10−3 | 1.1556 × 10−4 | 7.4454 × 10−8 | 5.2661 × 10−8 |
0.0005 | 5.6177 × 10−4 | 2.9965 × 10−5 | 2.1479 × 10−8 | 1.6911 × 10−8 |
0.00025 | 1.5380 × 10−4 | 9.9200 × 10−6 | 5.4476 × 10−9 | 5.1349 × 10−9 |
0.000125 | 3.9312 × 10−5 | 1.9910 × 10−6 | 1.9831 × 10−9 | 1.4734 × 10−9 |