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            <front>

                <journal-meta>
                                                                <journal-id>idu natural and applied sciences journal (idunas)</journal-id>
            <journal-title-group>
                                                                                    <journal-title>Natural and Applied Sciences Journal</journal-title>
            </journal-title-group>
                            <issn pub-type="ppub">2645-9000</issn>
                                                                                                        <publisher>
                    <publisher-name>İzmir Demokrasi Üniversitesi</publisher-name>
                </publisher>
                    </journal-meta>
                <article-meta>
                                        <article-id pub-id-type="doi">10.38061/idunas.1566513</article-id>
                                                                <article-categories>
                                            <subj-group  xml:lang="en">
                                                            <subject>Applied Mathematics (Other)</subject>
                                                    </subj-group>
                                            <subj-group  xml:lang="tr">
                                                            <subject>Uygulamalı Matematik (Diğer)</subject>
                                                    </subj-group>
                                    </article-categories>
                                                                                                                                                        <title-group>
                                                                                                                        <article-title>The Heat Problem with Non-Local Boundary Conditions</article-title>
                                                                                                                                        </title-group>
            
                                                    <contrib-group content-type="authors">
                                                                        <contrib contrib-type="author">
                                                                    <contrib-id contrib-id-type="orcid">
                                        https://orcid.org/0000-0002-1877-9791</contrib-id>
                                                                <name>
                                    <surname>Bağlan</surname>
                                    <given-names>İrem</given-names>
                                </name>
                                                                    <aff>kocaeli üniversitesi</aff>
                                                            </contrib>
                                                                                </contrib-group>
                        
                                        <pub-date pub-type="pub" iso-8601-date="20241227">
                    <day>12</day>
                    <month>27</month>
                    <year>2024</year>
                </pub-date>
                                        <volume>7</volume>
                                        <issue>2</issue>
                                        <fpage>61</fpage>
                                        <lpage>68</lpage>
                        
                        <history>
                                    <date date-type="received" iso-8601-date="20241013">
                        <day>10</day>
                        <month>13</month>
                        <year>2024</year>
                    </date>
                                                    <date date-type="accepted" iso-8601-date="20241112">
                        <day>11</day>
                        <month>12</month>
                        <year>2024</year>
                    </date>
                            </history>
                                        <permissions>
                    <copyright-statement>Copyright © 2018, Natural and Applied Sciences Journal</copyright-statement>
                    <copyright-year>2018</copyright-year>
                    <copyright-holder>Natural and Applied Sciences Journal</copyright-holder>
                </permissions>
            
                                                                                                <abstract><p>In this article, the two-dimensional inverse nonlinear parabolic problem is discussed. The most important feature of the problem was its solution with the Fourier approach. The solution was obtained by Fourier implicit and iteration method .</p></abstract>
                                                                                    
            
                                                            <kwd-group>
                                                    <kwd>The higher problem</kwd>
                                                    <kwd>  Fourier iterative method</kwd>
                                                    <kwd>  nonlocal conditions</kwd>
                                                    <kwd>  implicit finite-difference methods.</kwd>
                                            </kwd-group>
                                                        
                                                                                                                                                    </article-meta>
    </front>
    <back>
                            <ref-list>
                                    <ref id="ref1">
                        <label>1</label>
                        <mixed-citation publication-type="journal">1. Sharma, P.R., Methi, G. (2012). Solution of two-dimensional parabolic equation subject to non-local conditions using homotopy Perturbation method, Jour. of App.Com., 1, 12-16.</mixed-citation>
                    </ref>
                                    <ref id="ref2">
                        <label>2</label>
                        <mixed-citation publication-type="journal">2. Cannon, J. Lin, Y. (1899). Determination of parameter p(t) in Hölder classes for some semi-linear parabolic equations, Inverse Problems, 4, 595-606.</mixed-citation>
                    </ref>
                                    <ref id="ref3">
                        <label>3</label>
                        <mixed-citation publication-type="journal">3. Dehghan, M. (2005). Efficient techniques for the parabolic equation subject to nonlocal specifications, Applied Numerical Mathematics, 52(1), 39-62,2005.</mixed-citation>
                    </ref>
                                    <ref id="ref4">
                        <label>4</label>
                        <mixed-citation publication-type="journal">4. Dehghan, M. (2001). Implicit Solution of a Two-Dimensional Parabolic Inverse Problem with Temperature Overspecification, Journal of Computational Analysis and Applications, 3(4).
5. Bağlan, I., Kanca, F. (2020). Solution of the boundary-value problem of heat conduction with periodic boundary conditions, Ukrainian Mathematical Journal, 72(2), 232-245.</mixed-citation>
                    </ref>
                                    <ref id="ref5">
                        <label>5</label>
                        <mixed-citation publication-type="journal">6. Bağlan, I., Kanca, F. (2020). Two-dimensional inverse quasilinear parabolic problems with periodic boundary conditions of the boundary-value problem of heat conduction with periodic boundary conditions, Applicable Analysis, 98(8), 1549-1565.
7. Ionkin, N.I. (1977). Solution of a boundary value problem in heat conduction with a nonclassical boundary condition, Differential Equations, 13, 204-211.</mixed-citation>
                    </ref>
                                    <ref id="ref6">
                        <label>6</label>
                        <mixed-citation publication-type="journal">8. Hill G.W. (1886), On the part of the motion of the lunar perigee which is a function of the mean motions of the sun and moon, Acta Mathematica, 8,1-36.</mixed-citation>
                    </ref>
                            </ref-list>
                    </back>
    </article>
