\(\mathcal {E}_{1^{\prime }}\) | \(\mathcal {E}_{2^{\prime }}\) | \(\mathcal {E}_{3^{\prime }}\) | \(\mathcal {E}_{4^{\prime }}\) | \(\mathcal {E}_{5^{\prime }}\) | |
---|---|---|---|---|---|
(a) L=0 (no initial data) | |||||
Optimal | 1.2215 | 1.2305 | 1.2399 | 1.2433 | 1.2427 |
Approximate | 1.2246 | 1.2340 | 1.2388 | 1.2390 | 1.2416 |
(b) L=10 | |||||
Optimal | 1.1615 | 1.1736 | 1.1780 | 1.1790 | 1.1792 |
Approximate | 1.1646 | 1.1747 | 1.1767 | 1.1775 | 1.1779 |
(c) L=20 | |||||
Optimal | 1.1573 | 1.1660 | 1.1706 | 1.1720 | 1.1705 |
Approximate | 1.1598 | 1.1665 | 1.1701 | 1.1704 | 1.1695 |
(d) L=50 | |||||
Optimal | 1.1463 | 1.1534 | 1.1558 | 1.1560 | 1.1561 |
Approximate | 1.1487 | 1.1529 | 1.1557 | 1.1547 | 1.1557 |