Theory and Modern Applications
Table 4 Shishkin mesh, \(\tau _{\epsilon }=\min \{0.5,-\epsilon (p+1) \ln \epsilon \}\), \(\epsilon =10^{-8}\)
From: The coupled method for singularly perturbed Volterra integro-differential equations
N | p = 1 | p = 2 | p = 3 | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\|\cdot \|_{\infty }\) | order | \(\|\cdot \|_{L^{2}}\) | order | \(\|\cdot \|_{\infty }\) | order | \(\|\cdot \|_{L^{2}}\) | order | \(\|\cdot \|_{\infty }\) | order | \(\|\cdot \|_{L^{2}}\) | order | |
32 | 1.70e − 1 | 1.25 | 9.84e − 5 | 1.98 | 4.02e − 2 | 2.16 | 9.65e − 6 | 1.95 | 4.16e − 4 | 4.48 | 4.85e − 7 | 3.16 |
64 | 4.69e − 2 | 1.86 | 2.47e − 5 | 1.99 | 4.49e − 3 | 3.16 | 1.75e − 6 | 2.46 | 8.52e − 6 | 5.55 | 3.78e − 8 | 3.68 |
128 | 1.04e − 2 | 2.17 | 6.20e − 6 | 2.00 | 2.94e − 4 | 3.93 | 2.49e − 7 | 2.81 | 1.33e − 7 | 6.06 | 2.52e − 9 | 3.91 |
256 | 2.54e − 3 | 2.04 | 1.55e − 6 | 2.00 | 1.78e − 5 | 4.05 | 3.23e − 8 | 2.95 | 2.06e − 9 | 6.01 | 1.60e − 10 | 3.98 |