The Approximate Solution of Fredholm Integral Equations with Oscillatory Trigonometric Kernels

Table 3

Approximations for 𝑦(𝑥)+∫¹₋₁(𝑒^{𝑖𝜔(𝑥−𝑡)}/|𝑥−𝑡|^0.5)𝑦(𝑡)𝑑𝑡=𝑒^𝑥 with 𝜔=10⁶.

𝑥	cos(𝜋)	cos(3𝜋/4)	cos(0)
𝑦^41	0.367419631536920	0.491835233010361	0.997500711679274
𝑦^81	0.367419631541538	0.491835233006225	0.997500711679218
𝑦1^16	0.367419632527633	0.491835233064998	0.997500711678921
𝑦^42	0.000458466865252363	0.150404190×10^−5	−0.219327280×10^−5
𝑦^82	0.000458466860662437	0.150403636×10^−5	−0.219326739×10^−5
𝑦2^16	0.000458463698666909	0.150390826×10^−5	−0.219326736×10^−5