Theory and Modern Applications
Table 8 Approximations at \(\pmb{x=0.1,0.5,0.9}\) for \(\pmb{u(x)-\int_{-1}^{1}\frac{u(y)}{(y-x)}\,dy=f(x)}\)
From: Fast multipole method for singular integral equations of second kind
x | 0.1 | 0.5 | 0.9 |
|---|---|---|---|
\(\hat{u}_{10}\) | −0.025111748216482 | 0.052110055810136 | 0.363240467300408 |
\(\hat{u}_{100}\) | −0.001202605523378 | 0.101502077326766 | 0.409787561038363 |
\(\hat{u}_{1000}\) | 0.000783503911385 | 0.100161733460852 | 0.403492522553747 |
u | 0.000990099009901 | 0.1 | 0.402762430939227 |