Theory and Modern Applications
Table 1 Error norms for Problem 1 at \(t=1\) with \(N=100\), \(\alpha =1.75\)
Δt | Method in [1] | Proposed method | ||
|---|---|---|---|---|
\(L_{\infty }\) | \(L_{2}\) | \(L_{\infty }\) | \(L_{2}\) | |
0.001 | 1.8221 × 10−3 | 1.1556 × 10−4 | 1.5535 × 10−6 | 2.3182 × 10−7 |
0.0005 | 5.6177 × 10−4 | 2.9965 × 10−5 | 5.3380 × 10−7 | 6.2981 × 10−8 |
0.00025 | 1.5380 × 10−4 | 9.9200 × 10−6 | 1.9124 × 10−7 | 2.1050 × 10−8 |
0.000125 | 3.9312 × 10−5 | 1.9910 × 10−6 | 5.6215 × 10−8 | 6.4940 × 10−9 |