Theory and Modern Applications
Table 1 Maximum error \(E_{\varepsilon _{1},\varepsilon _{2}}^{N,M}\) for Example 5.1 using the adaptive grid method with \(\varepsilon _{1}=10^{-2}\)
\(\varepsilon _{2}\) | Number of intervals N/time size Δt | ||||
|---|---|---|---|---|---|
\(32/\frac{1}{20}\) | \(64/\frac{1}{40}\) | \(128/\frac{1}{80}\) | \(256/\frac{1}{160}\) | \(512/\frac{1}{320}\) | |
10−2 | 1.4250e − 01 | 7.9154e − 02 | 4.0946e − 02 | 1.9700e − 02 | 1.0618e − 02 |
10−3 | 1.1938e − 01 | 7.1365e − 02 | 4.0316e − 02 | 2.1692e − 02 | 1.1134e − 02 |
10−4 | 1.6654e − 01 | 9.3826e − 02 | 5.4498e − 02 | 2.7184e − 02 | 1.3513e − 02 |
10−5 | 1.8941e − 01 | 1.1599e − 01 | 6.5234e − 02 | 3.2013e − 02 | 1.7915e − 02 |
10−6 | 2.1617e − 01 | 1.4118e − 01 | 7.4591e − 02 | 3.9796e − 02 | 2.0694e − 02 |
10−7 | 2.4067e − 01 | 1.3939e − 01 | 7.0974e − 02 | 4.2329e − 02 | 2.3750e − 02 |