Theory and Modern Applications
Table 9 Rate of convergence \(r_{\varepsilon _{1},\varepsilon _{2}} ^{N,M}\) for Example 5.2 using the adaptive grid method with \(\varepsilon _{2}=10^{-2}\)
\(\varepsilon _{1}\) | Number of intervals N/time size Δt | |||
|---|---|---|---|---|
\(32/\frac{1}{20}\) | \(64/\frac{1}{40}\) | \(128/\frac{1}{80}\) | \(256/\frac{1}{160}\) | |
10−3 | 0.6415 | 0.7725 | 0.8504 | 0.9132 |
10−4 | 0.6533 | 0.7888 | 0.8853 | 0.9870 |
10−5 | 0.5850 | 0.7950 | 0.7919 | 0.8498 |
10−6 | 0.5783 | 0.7454 | 0.8093 | 0.7973 |
10−7 | 0.6467 | 0.5915 | 0.7870 | 0.7360 |