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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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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Abstract 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.
AbstractList 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.
Author Ma, Wenxiu
Khan, Suliman
SAIRA
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10.1007/BF01386223
10.1016/j.amc.2011.08.101
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CorporateAuthor School of mathematical sciences, Zhejiang Normal University, Jinhua, 321004, China
Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia
Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA
State Key Laboratory of Mechanics and Control for Aerospace Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China
School of Mathematical and Statistical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa
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SubjectTerms algebraic singularities
analytic function
gauss-laguerre quadrature
high oscillations
logarithmic singularity
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Title An efficient numerical method for highly oscillatory logarithmic-algebraic singular integrals
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