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<p>This work delves into the study of Fredholm integral equations of the second kind by using Franklin wavelet Galerkin method. We approximate the solution within the Galerkin and iterated Galerkin framework, where Franklin wavelets are used as bases. We discuss convergence analysis for both the methods in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> and infinity norm. We observe that the iterated Franklin wavelet Galerkin method improves over the Franklin wavelet Galerkin method. We perform numerical examples to justify the theoretical results.</p>

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Franklin wavelet Galerkin method for Fredholm integral equations of the second kind

  • 期刊论文

  • 发表日期：

    2025年11月21日

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  • Amarendra Malik,
  • Subhashree Patel,
  • Amaresh Chandra Panda

摘要

This work delves into the study of Fredholm integral equations of the second kind by using Franklin wavelet Galerkin method. We approximate the solution within the Galerkin and iterated Galerkin framework, where Franklin wavelets are used as bases. We discuss convergence analysis for both the methods in \(L^2\) L 2 and infinity norm. We observe that the iterated Franklin wavelet Galerkin method improves over the Franklin wavelet Galerkin method. We perform numerical examples to justify the theoretical results.