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Volume 18, Issue 3
Approximate Method for Computing Hypersingular Integrals with Oscillatory Kernels

Yuxin Zhang, Jin Li & Mengyao Yu

DOI: 10.4208/nmtma.OA-2024-0115

Numer. Math. Theor. Meth. Appl., 18 (2025), pp. 771-793.

Published online: 2025-09

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  • Abstract

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.

  • Keywords

Oscillatory kernel, composite rectangle rule, hypersingular integral, extrapolation method.

  • AMS Subject Headings

65R10, 65D30, 65D32, 42A50, 42B20, 65B05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-18-771, author = {Zhang , YuxinLi , Jin and Yu , Mengyao}, title = {Approximate Method for Computing Hypersingular Integrals with Oscillatory Kernels}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2025}, volume = {18}, number = {3}, pages = {771--793}, abstract = {

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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2024-0115}, url = {http://global-sci.org/intro/article_detail/nmtma/24327.html} }
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 -

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.

Zhang , YuxinLi , Jin and Yu , Mengyao. (2025). Approximate Method for Computing Hypersingular Integrals with Oscillatory Kernels. Numerical Mathematics: Theory, Methods and Applications. 18 (3). 771-793. doi:10.4208/nmtma.OA-2024-0115
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