Theory and Modern Applications
Table 2 Rate of convergence \(r_{\varepsilon _{1},\varepsilon _{2}} ^{N,M}\) for Example 5.1 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 | 0.8482 | 0.9509 | 1.0555 | 0.8917 |
10−3 | 0.7423 | 0.8239 | 0.8942 | 0.9622 |
10−4 | 0.8278 | 0.7838 | 1.0034 | 1.0084 |
10−5 | 0.7075 | 0.8303 | 1.0270 | 0.8375 |
10−6 | 0.6146 | 0.9205 | 0.9064 | 0.9434 |
10−7 | 0.7879 | 0.9738 | 0.7456 | 0.8337 |