Theory and Modern Applications
Table 7 Rate of convergence \(r_{\varepsilon _{1},\varepsilon _{2}} ^{N,M}\) for Example 5.2 using the adaptive grid method with \(\varepsilon _{1}=10^{-2}\)
\(\varepsilon _{2}\) | Number of intervals N/time size Δt | |||
|---|---|---|---|---|
\(32/\frac{1}{20}\) | \(64/\frac{1}{40}\) | \(128/\frac{1}{80}\) | \(256/\frac{1}{160}\) | |
10−2 | 0.6567 | 0.7866 | 0.8619 | 0.9471 |
10−3 | 0.6927 | 0.7566 | 0.8428 | 0.9109 |
10−4 | 0.7062 | 0.7981 | 0.8949 | 0.9913 |
10−5 | 0.6289 | 0.8009 | 0.8017 | 0.7629 |
10−6 | 0.6168 | 0.7484 | 0.8355 | 0.7946 |
10−7 | 0.6718 | 0.6448 | 0.7960 | 0.6836 |