1 Ocak 2013 Dergi makalesi Açık Erişim

Demir, Ali; Erman, Sertac; Ozgur, Berrak; Korkmaz, Esra

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  <identifier identifierType="URL">https://aperta.ulakbim.gov.tr/record/12375</identifier>
  <creators>
    <creator>
      <creatorName>Demir, Ali</creatorName>
      <givenName>Ali</givenName>
      <familyName>Demir</familyName>
      <affiliation>Kocaeli Univ Umuttepe, Dept Math, TR-41380 Izmit, Kocaeli, Turkey</affiliation>
    </creator>
    <creator>
      <creatorName>Erman, Sertac</creatorName>
      <givenName>Sertac</givenName>
      <familyName>Erman</familyName>
      <affiliation>Kocaeli Univ Umuttepe, Dept Math, TR-41380 Izmit, Kocaeli, Turkey</affiliation>
    </creator>
    <creator>
      <creatorName>Ozgur, Berrak</creatorName>
      <givenName>Berrak</givenName>
      <familyName>Ozgur</familyName>
      <affiliation>Kocaeli Univ Umuttepe, Dept Math, TR-41380 Izmit, Kocaeli, Turkey</affiliation>
    </creator>
    <creator>
      <creatorName>Korkmaz, Esra</creatorName>
      <givenName>Esra</givenName>
      <familyName>Korkmaz</familyName>
      <affiliation>Ardahan Univ, TR-75000 Merkez, Ardahan, Turkey</affiliation>
    </creator>
  </creators>
  <titles>
    <title>Analysis Of The New Homotopy Perturbation Method For Linear And Nonlinear Problems</title>
  </titles>
  <publisher>Aperta</publisher>
  <publicationYear>2013</publicationYear>
  <dates>
    <date dateType="Issued">2013-01-01</date>
  </dates>
  <resourceType resourceTypeGeneral="Text">Journal article</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://aperta.ulakbim.gov.tr/record/12375</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.1186/1687-2770-2013-61</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="http://www.opendefinition.org/licenses/cc-by">Creative Commons Attribution</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
  </rightsList>
  <descriptions>
    <description descriptionType="Abstract">In this article, a new homotopy technique is presented for the mathematical analysis of finding the solution of a first-order inhomogeneous partial differential equation (PDE) u(x)(x, y) + a(x, y)u(y)(x, y) + b(x, y)g(u) = f(x, y). The homotopy perturbation method (HPM) and the decomposition of a source function are used together to develop this new technique. The homotopy constructed in this technique is based on the decomposition of a source function. Various decompositions of source functions lead to various homotopies. Using the fact that the decomposition of a source function affects the convergence of a solution leads us to development of a new method for the decomposition of a source function to accelerate the convergence of a solution. The purpose of this study is to show that constructing the proper homotopy by decomposing f (x, y) in a correct way determines the solution with less computational work than using the existing approach while supplying quantitatively reliable results. Moreover, this method can be generalized to all inhomogeneous PDE problems.</description>
  </descriptions>
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