Theory and Modern Applications
Table 8 Maximum error \(E_{\varepsilon }^{N,M}\) for Example 5.2 using the adaptive grid method with \(\varepsilon _{2}=10^{-2}\)
\(\varepsilon _{1}\) | Number of intervals N/time size Δt | ||||
|---|---|---|---|---|---|
\(32/\frac{1}{20}\) | \(64/\frac{1}{40}\) | \(128/\frac{1}{80}\) | \(256/\frac{1}{160}\) | \(512/\frac{1}{320}\) | |
10−3 | 8.5765e − 02 | 5.4978e − 02 | 3.2185e − 02 | 1.7851e − 02 | 9.4792e − 03 |
10−4 | 1.0625e − 01 | 6.7554e − 02 | 3.9103e − 02 | 2.1170e − 02 | 1.0681e − 02 |
10−5 | 1.1804e − 01 | 7.8694e − 02 | 4.5355e − 02 | 2.6197e − 02 | 1.4536e − 02 |
10−6 | 1.1955e − 01 | 8.0068e − 02 | 4.7762e − 02 | 2.7255e − 02 | 1.5683e − 02 |
10−7 | 1.1639e − 01 | 7.4345e − 02 | 4.9340e − 02 | 2.8595e − 02 | 1.7408e − 02 |