The Approximate Solution of Fredholm Integral Equations with Oscillatory Trigonometric Kernels

Table 1

Approximations for 𝑦(𝑥)+∫¹₋₁(𝑒^{𝑖𝜔(𝑥−𝑡)}/|𝑥−𝑡|^0.5)𝑦(𝑡)𝑑𝑡=𝑒^𝑥 with 𝜔=10³.

𝑥	cos(𝜋)	cos(3𝜋/4)	cos(0)
𝑦^41	0.351696035495271	0.459037927481918	0.924223909091303
𝑦^81	0.351696947581043	0.459033811940511	0.924224547405338
𝑦1^16	0.351741610883315	0.459036527929146	0.924226969620880
𝑦^42	0.0141286409694892	0.000146310591227839	−0.00107727880701281
𝑦^82	0.0141193392298137	0.000145019893750479	−0.00107593754108643
𝑦2^16	0.0140583682955762	0.000144178555797097	−0.00106881635211410