Approximate Method to Compute Hypersingular Finite-Part Integrals with Rapidly Oscillating Kernels



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Submitted Jul 10, 2023
Published Sep 29, 2023
10.24018/ejmath.2023.4.5.283

Abstract viewed = 185 times

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In this paper, an algorithm for the numerical evaluation of hypersingular finite-part integrals with rapidly oscillating kernels is proposed. The method is based on an interpolatory procedure at zeros of the orthogonal polynomials with respect to the first kind Chebyshev weight. Bounds of the error and of the amplification factor are also provided. Numerically stable procedures are obtained and the corresponding algorithms can be implemented in a fast way.

Keywords: Error bound Finite-part integral Oscillatory integral Stability

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