The Approximate Solution of Fredholm Integral Equations with Oscillatory Trigonometric Kernels

Table 2

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/4)	1
𝑦^41	1.88249404678421	2.61059423521207
𝑦^81	1.88248275737555	2.61059120470589
𝑦1^16	1.88248361661370	2.61073031676337
𝑦^42	0.00323202027752064	−0.0995508315886191
𝑦^82	0.00321634589900894	−0.0994917961267987
𝑦2^16	0.00319500282444326	−0.0993143176430846