Theory and Modern Applications
Table 6 Maximum error \(E_{\varepsilon }^{N,M}\) for Example 5.2 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 | 7.5287e − 02 | 4.7758e − 02 | 2.7686e − 02 | 1.5234e − 02 | 7.9016e − 03 |
10−3 | 8.0020e − 02 | 4.9508e − 02 | 2.9305e − 02 | 1.6339e − 02 | 8.6897e − 03 |
10−4 | 1.1255e − 01 | 6.8986e − 02 | 3.9675e − 02 | 2.1337e − 02 | 1.0733e − 02 |
10−5 | 1.2378e − 01 | 8.0042e − 02 | 4.5942e − 02 | 2.6356e − 02 | 1.5532e − 02 |
10−6 | 1.2592e − 01 | 8.2114e − 02 | 4.8879e − 02 | 2.7391e − 02 | 1.5791e − 02 |
10−7 | 1.2119e − 01 | 7.6072e − 02 | 4.8654e − 02 | 2.8021e − 02 | 1.7446e − 02 |