Theory and Modern Applications
Table 7 Improved graded mesh, \(\lambda =2\), \(\tau _{\epsilon }= \min \{0.5,-\epsilon (p+1)\ln \epsilon \}\), \(\epsilon =10^{-6}\)
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 | 9.69e − 3 | 2.04 | 9.65e − 5 | 2.00 | 2.50e − 4 | 3.84 | 1.89e − 6 | 2.98 | 1.15e − 7 | 5.55 | 1.33e − 8 | 3.97 |
64 | 2.43e − 3 | 2.00 | 2.41e − 5 | 2.00 | 1.62e − 5 | 3.95 | 2.37e − 7 | 2.99 | 1.82e − 9 | 5.98 | 8.36e − 10 | 3.99 |
128 | 6.09e − 4 | 2.00 | 6.03e − 6 | 2.00 | 1.02e − 6 | 3.99 | 2.97e − 8 | 3.00 | 2.85e − 11 | 6.00 | 5.23e − 11 | 4.00 |
256 | 1.52e − 4 | 2.00 | 1.51e − 6 | 2.00 | 6.37e − 8 | 4.00 | 3.72e − 9 | 3.00 | 4.46e − 13 | 6.00 | 3.27e − 12 | 4.00 |