Piecewise Linear Maximum Entropy Method for Fredholm Integral Equations with Weakly Singular Kernel

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Abstract

Approximate solution of Fredholm integral equations with certain types of weakly singular algebraic kernels is obtained by the piecewise linear maximum entropy method. During implementation of the method, two-dimension numerical integration is reduced to one-dimension numerical integration, which allows to lower the computational cost. The results of numerical experiments are consistent with theoretical findings and show the effectiveness of the method.

Keywords:

Fredholm integral equation piecewise linear maximum entropy method weakly singular kernel

Author Biographies

  • Yucheng Song
    Department of Mathematics, Zhejiang University of Finance & Economics Dongfang College, Haining 314408, China
  • Tingting Li
    Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, China
  • Jiu Ding

    School of Mathematics and Natural Sciences, The University of Southern Mississippi, Hattiesburg, MS 39406-5043, USA

    School of Mathematics and Statistics, Nanfang College Guangzhou, Guangzhou 510970, China

  • Congming Jin
    Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, China
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DOI

10.4208/eajam.2025-140.241225