U. V

A GENOCCHI WAVELET METHOD FOR HIGHLY OSCILLATORY INTEGRALS WITH AN ENDPOINT SINGULARITY

This study introduces an efficient high-order wavelet quadrature technique for computing highly oscillatory integrals affected by endpoint singular behavior of the form: 𝑙⁢𝑎⁢𝑡⁢𝑒⁢𝑥⁢∫1 0𝑓⁡(𝑥)⁢sin⁡( 𝜔 𝑥𝑟 )𝑑𝑥 and ∫1 0𝑓⁡(𝑥)⁢cos⁡( 𝜔 𝑥𝑟 )𝑑𝑥,𝜔 ≫1,𝑟 >0, where standard numerical methods often lose stability and accuracy due to i...