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Theory and Modern Applications

Table 6 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

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

0.057786709933708

0.465859007671879

0.872182894009698

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

0.106011730395414

0.507142753891225

0.908324232818361

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

0.100609029282889

0.500725569118200

0.900861403735125

u

0.1

0.5

0.9