Abstract
In this paper, we are concerned with the numerical approximations of one-sided Hilbert transforms with oscillatory kernel by means of the multiple integrals. This type of Hilbert transform has two computing difficulties: singularity and oscillation. To avoid the singularity, we transfer the Hilbert transform to an individual oscillatory integral which can be analytically calculated and a non-singular integral which can be well evaluated by the multiple integrals. Numerical examples are provided to illustrate the advantages of the proposed methods.
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Communicated by Hui Liang.
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The work is supported by Natural Science Foundation of Guangdong Province, China (No. 2015A030313615).
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Chen, R., Yu, D. & Chen, J. Numerical approximations of highly oscillatory Hilbert transforms. Comp. Appl. Math. 39, 180 (2020). https://doi.org/10.1007/s40314-020-01193-9
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DOI: https://doi.org/10.1007/s40314-020-01193-9