Theory and Modern Applications
Table 10 Maximum absolute errors (\(L_{\infty}\)) for Example 3 at \(t=0.1\) when \(\alpha=0.9\), \(n=10\), \(\Delta t= 0.001\), and \(z \in [0,\pi]\)
z | Exact solution | Approximate solution | \(L_{\infty}\)-norm |
|---|---|---|---|
\(\frac{\pi}{10}\) | 0.00309017 | 0.00317619 | 8.6021 × 10−5 |
\(\frac{\pi}{5}\) | 0.00587785 | 0.00604098 | 1.6313 × 10−4 |
\(\frac{3\pi}{10}\) | 0.00809017 | 0.00831405 | 2.2388 × 10−4 |
\(\frac{2\pi}{5}\) | 0.00951057 | 0.00977324 | 2.6268 × 10−4 |
\(\frac{\pi}{2}\) | 0.01000000 | 0.01027600 | 2.7604 × 10−4 |
\(\frac{3\pi}{5}\) | 0.00951057 | 0.00977324 | 2.6268 × 10−4 |
\(\frac{7\pi}{10}\) | 0.00809017 | 0.00831405 | 2.2388 × 10−4 |
\(\frac{4\pi}{5}\) | 0.00587785 | 0.00604098 | 1.6313 × 10−4 |
\(\frac{9\pi}{10}\) | 0.00309017 | 0.00317619 | 8.6021 × 10−5 |