Table 1 Maximum absolute error of Example 4.1 for \(\delta =0.9\varepsilon\), \(\theta =\frac{1}{2}\)
From: Accurate numerical scheme for singularly perturbed parabolic delay differential equation
\(\varepsilon \; \downarrow \; N=M\rightarrow\) | \(2^4\) | \(2^5\) | \(2^6\) | \(2^7\) |
|---|---|---|---|---|
Before extrapolation | ||||
\(10^{-4}\) | 1.4608e−02 | 8.1605e−03 | 4.3079e−03 | 2.2125e−03 |
\(10^{-6}\) | 1.4608e−02 | 8.1600e−03 | 4.3077e−03 | 2.2124e−03 |
\(10^{-8}\) | 1.4608e−02 | 8.1600e−03 | 4.3077e−03 | 2.2124e−03 |
\(10^{-10}\) | 1.4608e−02 | 8.1600e−03 | 4.3077e−03 | 2.2124e−03 |
\(E^{N,M}\) | 1.4608e−02 | 8.1600e−03 | 4.3077e−03 | 2.2124e−03 |
\(r^{N,M}\) | 0.8401 | 0.9217 | 0.9613 | - |
After extrapolation | ||||
\(10^{-4}\) | 8.1605e−03 | 2.2125e−03 | 5.6425e−04 | 1.4182e−04 |
\(10^{-6}\) | 8.1600e−03 | 2.2124e−03 | 5.6422e−04 | 1.4181e−04 |
\(10^{-8}\) | 8.1600e−03 | 2.2124e−03 | 5.6422e−04 | 1.4181e−04 |
\(10^{-10}\) | 8.1600e−03 | 2.2124e−03 | 5.6422e−04 | 1.4181e−04 |
\(E^{N,M}\) | 8.1605e−03 | 2.2125e−03 | 5.6425e−04 | 1.4182e−04 |
\(r^{N,M}\) | 1.8830 | 1.9713 | 1.9923 | – |