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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… Click to show full 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.
Journal Title: Computational and Applied Mathematics
Year Published: 2020
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