Theory and Modern Applications
Table 3 Shishkin mesh, \(\tau _{\epsilon }=\min \{0.5,-\epsilon (p+1) \ln \epsilon \}\), \(\epsilon =10^{-6}\)
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 | 1.05e − 1 | 1.51 | 1.66e − 4 | 1.83 | 1.75e − 2 | 2.59 | 4.94e − 5 | 2.17 | 9.06e − 5 | 4.98 | 1.73e − 6 | 3.42 |
64 | 2.48e − 2 | 2.08 | 4.32e − 5 | 1.94 | 1.53e − 3 | 3.52 | 7.94e − 6 | 2.64 | 1.54e − 6 | 5.88 | 1.24e − 7 | 3.80 |
128 | 5.78e − 3 | 2.10 | 1.09e − 5 | 1.98 | 8.88e − 5 | 4.10 | 1.07e − 6 | 2.89 | 2.36e − 8 | 6.03 | 8.05e − 9 | 3.95 |
256 | 1.43e − 3 | 2.01 | 2.74e − 6 | 2.00 | 5.65e − 6 | 3.97 | 1.37e − 7 | 2.97 | 3.69e − 10 | 6.00 | 5.08e − 10 | 3.99 |