1 Ocak 2013 Dergi makalesi Açık Erişim

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

Citation Style Language JSON

{
  "DOI": "10.1186/1687-2770-2013-61", 
  "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.", 
  "author": [
    {
      "family": "Demir", 
      "given": " Ali"
    }, 
    {
      "family": "Erman", 
      "given": " Sertac"
    }, 
    {
      "family": "Ozgur", 
      "given": " Berrak"
    }, 
    {
      "family": "Korkmaz", 
      "given": " Esra"
    }
  ], 
  "container_title": "BOUNDARY VALUE PROBLEMS", 
  "id": "12375", 
  "issued": {
    "date-parts": [
      [
        2013, 
        1, 
        1
      ]
    ]
  }, 
  "title": "Analysis of the new homotopy perturbation method for linear and nonlinear problems", 
  "type": "article-journal"
}