数学季刊 ›› 2026, Vol. 41 ›› Issue (3): 299-306.doi: 10.13371/j.cnki.chin.q.j.m.2026.03.005

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一种求解具有退化核的Hammerstein积分方程精确解的新方法

  

  1. 1 . School of Mathematics and Statistics, Henan University, Kaifeng 475004, China; 2. Center for Applied Mathematics of Henan Province, Henan University, Zhengzhou 450046, China
  • 收稿日期:2026-02-01 出版日期:2026-09-30 发布日期:2026-09-30
  • 作者简介:HU Jin-dou (2002-), male, native of Shijiazhuang, Hebei, graduate student of Henan University; YAN Li-na (2003-), female, native of Xinxiang, Henan, graduate student of Henan University; HUANG Qiong-ao (1990-), male, native of Zhoukou, Henan, associate professor of Henan University, engages in numerical methods of PDEs. 
  • 基金资助:

A Novel Method for Exact Solutions of Hammerstein Integral Equations with Degenerate Kernels 

  1. 1 . School of Mathematics and Statistics, Henan University, Kaifeng 475004, China; 2. Center for Applied Mathematics of Henan Province, Henan University, Zhengzhou 450046, China
  • Received:2026-02-01 Online:2026-09-30 Published:2026-09-30
  • About author:HU Jin-dou (2002-), male, native of Shijiazhuang, Hebei, graduate student of Henan University; YAN Li-na (2003-), female, native of Xinxiang, Henan, graduate student of Henan University; HUANG Qiong-ao (1990-), male, native of Zhoukou, Henan, associate professor of Henan University, engages in numerical methods of PDEs. 

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摘要： This paper presents a novel analytical method for obtaining exact solutions of  Hammerstein integral equations with degenerate kernels. Subsequently, this approach is  systematically extended to equations with general kernels, yielding a convergent numerical  approximation whose theoretical analysis establishes sufficient conditions for convergence  and provides explicit error bounds. Numerical experiments are conducted to demonstrate the efficiency and accuracy of the proposed method, showing favorable performance compared to existing techniques.

关键词: Hammerstein integral equation, Degenerate kernel, Exact solution, Numerical , solution, Error analysis

Abstract: This paper presents a novel analytical method for obtaining exact solutions of  Hammerstein integral equations with degenerate kernels. Subsequently, this approach is  systematically extended to equations with general kernels, yielding a convergent numerical  approximation whose theoretical analysis establishes sufficient conditions for convergence  and provides explicit error bounds. Numerical experiments are conducted to demonstrate the efficiency and accuracy of the proposed method, showing favorable performance compared to existing techniques.

Key words: Hammerstein integral equation, Degenerate kernel, Exact solution, Numerical , solution, Error analysis

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