Table 2 Error estimates for the POD-Galerkin-Crank-Nicolson scheme (5.20) to the Eq. (6.4) at \(t=10\) with \(h=0.01\), \(k=0.05\)
d | \(k(\sum_{j=d+1}^{\ell}\lambda _{j})^{1/2}\) | \(\|u^{n}-u_{d}^{n}\|_{\infty}\) | Ratio |
|---|---|---|---|
2 | 2.8783 × 10−4 | 5.8492 × 10−9 | 2.0255 × 10−6 |
4 | 1.8863 × 10−4 | 5.8043 × 10−9 | 2.0814 × 10−6 |
6 | 1.3610 × 10−4 | 5.7050 × 10−9 | 2.0851 × 10−6 |
8 | 1.0902 × 10−4 | 5.6895 × 10−9 | 2.1001 × 10−6 |
10 | 8.1327 × 10−5 | 5.6828 × 10−9 | 2.1194 × 10−6 |
12 | 5.3441 × 10−5 | 5.6779 × 10−9 | 2.1398 × 10−6 |
14 | 3.9221 × 10−5 | 5.6678 × 10−9 | 2.1475 × 10−6 |
16 | 2.5628 × 10−5 | 5.6641 × 10−9 | 2.1532 × 10−6 |