TY - JOUR
T1 - Approximate Method for Computing Hypersingular Integrals with Oscillatory Kernels
AU - Zhang , Yuxin
AU - Li , Jin
AU - Yu , Mengyao
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 771
EP - 793
PY - 2025
DA - 2025/09
SN - 18
DO - http://doi.org/10.4208/nmtma.OA-2024-0115
UR - https://global-sci.org/intro/article_detail/nmtma/24327.html
KW - Oscillatory kernel, composite rectangle rule, hypersingular integral, extrapolation method.
AB - <p style="text-align: justify;">An extrapolation method is proposed for the numerical computation of
hypersingular integrals with oscillatory kernels. The oscillatory integral is reformulated as the weighted integral of a Hadamard finite part, which is subsequently
approximated using the weighted trapezoidal rule. The asymptotic expansion of the
error function is derived, and both the convergence order and the posterior error of
the algorithm are analyzed. Numerical examples verify the theoretical results and
demonstrate the validity of the proposed method.</p>