An efficient numerical method for highly oscillatory logarithmic-algebraic singular integrals

This paper discussed the numerical evaluation of highly oscillatory integrals involving logarithmic and algebraic singularities. For an analytic function in a sufficiently large region containing $ [a, b] $, the integral was transformed into the sum of two line integrals where the integrands did not...

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Bibliographic Details
Published inAIMS mathematics Vol. 10; no. 3; pp. 4899 - 4914
Main Authors SAIRA, Ma, Wenxiu, Khan, Suliman
Format Journal Article
LanguageEnglish
Published AIMS Press 01.03.2025
Subjects
algebraic singularities
analytic function
gauss-laguerre quadrature
high oscillations
logarithmic singularity
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ISSN2473-6988
2473-6988
DOI10.3934/math.2025224

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Summary:This paper discussed the numerical evaluation of highly oscillatory integrals involving logarithmic and algebraic singularities. For an analytic function in a sufficiently large region containing $ [a, b] $, the integral was transformed into the sum of two line integrals where the integrands did not oscillate and decay exponentially. Thus, to approximate the line integrals, generalized Gauss-Laguerre quadrature and logarithmic Gauss-Laguerre quadrature were applied. The error bound and numerical results demonstrated that the proposed method efficiently obtained high-precision results even for high oscillations.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2025224