Theory and Modern Applications
Table 1 Approximations at \(\pmb{x=-0.9,-0.5,-0.1}\) for \(\pmb{u(x)-\frac{1}{2\pi}\int_{-1}^{1}\frac{u(y)}{(y-x)}\,dy=f(x)}\)
From: Fast multipole method for singular integral equations of second kind
x | −0.9 | −0.5 | −0.1 |
|---|---|---|---|
\(\hat{u}_{10}\) | 1.000000000008664 | 0.999999999966656 | 1.000000002837690 |
\(\hat{u}_{100}\) | 0.999999988989405 | 0.999999996983473 | 0.999999998141215 |
\(\hat{u}_{1000}\) | 1.000000006379357 | 0.999999997488601 | 0.999999998811889 |
u | 1 | 1 | 1 |