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Theory and Modern Applications

Table 4 Approximations at \(\pmb{x=0.1,0.5,0.9}\) for \(\pmb{u(x)-\frac{1}{2\pi}\int_{-1}^{1}\frac{u(y)}{(y-x)^{2}}\,dy=f(x)}\)

From: Fast multipole method for singular integral equations of second kind

x

0.1

0.5

0.9

\(\hat{u}_{10}\)

0.999999917999549

0.999999981428145

0.999999993535332

\(\hat{u}_{100}\)

0.999999990036579

0.999999988582430

0.999999992194477

\(\hat{u}_{1000}\)

0.999999993375294

0.999999992061794

0.999999995726361

u

1

1

1