Theory and Modern Applications
Table 3 Approximations at \(\pmb{x=-0.9,-0.5,-0.1}\) for \(\pmb{u(x)-\frac{1}{2\pi}\int_{-1}^{1}\frac{u(y)}{(y-x)^{2}}\,dy=f(x)}\)
From: Fast multipole method for singular integral equations of second kind
x | −0.9 | −0.5 | −0.1 |
|---|---|---|---|
\(\hat{u}_{10}\) | 0.999999993535333 | 0.999999981428145 | 0.999999917999549 |
\(\hat{u}_{100}\) | 0.999999993845970 | 0.999999988715871 | 0.999999990115998 |
\(\hat{u}_{1000}\) | 0.999999995690078 | 0.999999991935489 | 0.999999993153335 |
u | 1 | 1 | 1 |