<?xml version="1.0" encoding="UTF-8"?>
<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-interdisciplinary-mathematics</journal-id>
      <journal-title-group>
        <journal-title>Journal of Interdisciplinary Mathematics</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-012X</issn>
      <issn publication-format="print">0972-0502</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.47974/JIM-2225</article-id>
      <title-group>
        <article-title>Proposing an effective numerical algorithm based on analysis to solve two-dimensional Friedholm equations</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Raheem</surname>
            <given-names>Muna Jaafar</given-names>
          </name>
          <aff>Department of Computer Science, College of Science, Mustensiriyah University, Baghdad, Iraq</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Abbas</surname>
            <given-names>Basim K.</given-names>
          </name>
          <aff>Department of Computer Science, College of Science, Mustensiriyah University, Baghdad, Iraq</aff>
        </contrib>
      </contrib-group>
      <volume>28</volume>
      <issue>3-B</issue>
      <fpage>1145</fpage>
      <lpage>1154</lpage>
      <pub-date date-type="pub">
        <day>08</day>
        <month>05</month>
        <year>2025</year>
      </pub-date>
      <abstract>
        <p>In order to solve 2-Dimention Fredholm integral formulas, a brand-new and effective numerical approach based on interpolating scaled functions is devised. FIE simplifies to the set for algebraic equation which solved to approximate the solution using functional matrices of integral for combining scaling variables. A convergence method is examined, and certain numerical tests support the precision and applicability of the approach. We contrast the proposed strategy with others to demonstrate its effectiveness.</p>
      </abstract>
      <kwd-group>
        <kwd>Dimention friedholm integral equations</kwd>
        <kwd>Scaled functions</kwd>
        <kwd>The functional matrices of integral</kwd>
        <kwd>Legendre equations</kwd>
      </kwd-group>
      <custom-meta-group>
        <custom-meta>
          <meta-name>access</meta-name>
          <meta-value>open</meta-value>
        </custom-meta>
        <custom-meta>
          <meta-name>retracted</meta-name>
          <meta-value>no</meta-value>
        </custom-meta>
      </custom-meta-group>
    </article-meta>
  </front>
</article>
