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<p>Many physical problems, initially formulated as initial or boundary value problems, are often addressed by converting them into integral equations defined on unbounded intervals. This paper introduces polynomial-based projection and modified projection methods for solving <i>Hammerstein</i> integral equations on the half-line with sufficiently smooth kernels. The approach employs either orthogonal or interpolatory projection using a <i>Laguerre</i> polynomial basis. We analyze the convergence of the approximate solution and establish its convergence rate. Numerical experiments are conducted to evaluate the effectiveness of the proposed methods in comparison to other approaches.</p>

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Laguerre spectral methods for nonlinear-Hammerstein integral equations on unbounded intervals

  • 期刊论文

  • 发表日期：

    2026年4月28日

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  • Hamza Bouda,
  • Chafik Allouch,
  • Ahmed Boujraf,
  • Zakaria El Allali,
  • Kapil Kant,
  • Mohamed Tahrichi

摘要

Many physical problems, initially formulated as initial or boundary value problems, are often addressed by converting them into integral equations defined on unbounded intervals. This paper introduces polynomial-based projection and modified projection methods for solving Hammerstein integral equations on the half-line with sufficiently smooth kernels. The approach employs either orthogonal or interpolatory projection using a Laguerre polynomial basis. We analyze the convergence of the approximate solution and establish its convergence rate. Numerical experiments are conducted to evaluate the effectiveness of the proposed methods in comparison to other approaches.