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This paper introduces an application of the Modified Jacobi-Galerkin method to address mixed-type Urysohn integral equations. Through rigorous analysis, the convergency of the proposed method is explored, with particular emphasis on establishing the existence and uniqueness theorems for approximate solutions. Convergence outcomes are investigated for both infinity and weighted \(L^2\) -norm. Additionally, a novel one-step iterated approximation technique is examined, and the superior superconvergence of the iterated modified Jacobi-Galerkin approximation is demonstrated.

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Multi-galerkin Method for Mixed-Type Urysohn Integral Equation Using Jacobi Polynomials

  • 会议论文

  • 发表日期：

    2026年

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  • Payel Das,
  • Mrinal Jana,
  • Kapil Kant

摘要

This paper introduces an application of the Modified Jacobi-Galerkin method to address mixed-type Urysohn integral equations. Through rigorous analysis, the convergency of the proposed method is explored, with particular emphasis on establishing the existence and uniqueness theorems for approximate solutions. Convergence outcomes are investigated for both infinity and weighted \(L^2\) -norm. Additionally, a novel one-step iterated approximation technique is examined, and the superior superconvergence of the iterated modified Jacobi-Galerkin approximation is demonstrated.