Table 2 Maximum absolute error of Example 4.2 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 | ||||
\(10^{-4}\) | 9.2814e−03 | 6.5095e−03 | 3.8026e−03 | 2.0167e−03 |
\(10^{-6}\) | 9.2806e−03 | 6.5094e−03 | 3.8028e−03 | 2.0170e−03 |
\(10^{-8}\) | 9.2806e−03 | 6.5094e−03 | 3.8028e−03 | 2.0170e−03 |
\(10^{-10}\) | 9.2806e−03 | 6.5094e−03 | 3.8028e−03 | 2.0170e−03 |
\(E^{N,M}\) | 9.2814e−03 | 6.5095e−03 | 3.8028e−03 | 2.0170e−03 |
\(r^{N,M}\) | 0.5118 | 0.7755 | 0.9149 | – |
After extrapolation | ||||
\(10^{-4}\) | 6.5095e−03 | 2.0167e−03 | 5.1663e−04 | 1.2977e−04 |
\(10^{-6}\) | 6.5094e−03 | 2.0170e−03 | 5.1667e−04 | 1.2978e−04 |
\(10^{-8}\) | 6.5094e−03 | 2.0170e−03 | 5.1667e−04 | 1.2978e−04 |
\(10^{-10}\) | 6.5094e−03 | 2.0170e−03 | 5.1667e−04 | 1.2978e−04 |
\(E^{N,M}\) | 7.0289e−03 | 2.0310e−03 | 5.1667e−04 | 1.2978e−04 |
\(r^{N,M}\) | 1.7911 | 1.9749 | 1.9932 | – |