Theory and Modern Applications
Table 3 Maximum error \(E_{\varepsilon }^{N,M}\) for Example 5.1 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 | 1.5659e − 01 | 9.0728e − 02 | 4.9472e − 02 | 2.5685e − 02 | 1.3157e − 02 |
10−4 | 1.6708e − 01 | 9.6715e − 02 | 5.2283e − 02 | 2.7677e − 02 | 1.4250e − 02 |
10−5 | 1.8039e − 01 | 9.7457e − 02 | 5.2987e − 02 | 2.8267e − 02 | 1.5248e − 02 |
10−6 | 1.7981e − 01 | 9.7493e − 02 | 5.3310e − 02 | 2.8267e − 02 | 1.6714e − 02 |
10−7 | 1.8023e − 01 | 1.0099e − 01 | 5.3679e − 02 | 2.8865e − 02 | 1.6969e − 02 |