Theory and Modern Applications
Table 2 Approximations at \(\pmb{x=0.1,0.5,0.9}\) 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 | 0.1 | 0.5 | 0.9 |
|---|---|---|---|
\(\hat{u}_{10}\) | 0.999999996078344 | 1.000000000199640 | 1.000000000023095 |
\(\hat{u}_{100}\) | 1.000000000689915 | 1.000000003352249 | 1.000000033188974 |
\(\hat{u}_{1000}\) | 1.000000000150622 | 1.000000002673433 | 0.999999995294152 |
u | 1 | 1 | 1 |