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<p>In this study, we present a comprehensive error analysis for second-order linear Fredholm–Stieltjes integral equations (SOLFSIEs), addressing a crucial aspect of approximation theory and numerical analysis. We derive explicit and practical error bounds, providing clear theoretical guarantees for the accuracy of numerical solutions. To substantiate our results, we perform rigorous numerical experiments, consistently demonstrating that increasing the discretization parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>n</mi> </math></EquationSource> </InlineEquation> leads to a systematic and predictable reduction in error. Our analysis covers a broad range of scenarios, including both separable and non-separable kernels, emphasizing the robustness and versatility of our approach. The findings affirm the reliability of our error estimation framework and highlight its strong potential for solving SOLFSIEs with high precision across diverse applications.</p>

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Error analysıs of the second-order lınear fredholm–stıeltjes ıntegral equatıon

  • 期刊论文

  • 发表日期：

    2025年6月12日

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  • Ramzan Ali,
  • Mukhammadmuso Abduzhabbarov,
  • Avyt Asanov

摘要

In this study, we present a comprehensive error analysis for second-order linear Fredholm–Stieltjes integral equations (SOLFSIEs), addressing a crucial aspect of approximation theory and numerical analysis. We derive explicit and practical error bounds, providing clear theoretical guarantees for the accuracy of numerical solutions. To substantiate our results, we perform rigorous numerical experiments, consistently demonstrating that increasing the discretization parameter \(n\) n leads to a systematic and predictable reduction in error. Our analysis covers a broad range of scenarios, including both separable and non-separable kernels, emphasizing the robustness and versatility of our approach. The findings affirm the reliability of our error estimation framework and highlight its strong potential for solving SOLFSIEs with high precision across diverse applications.