Solution of the two-dimensional heat equation for a square in terms of elliptic functions

Kurt N.

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, cilt.345, sa.3, ss.303-317, 2008 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 345 Sayı: 3
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1016/j.jfranklin.2007.09.003
  • Dergi Adı: JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.303-317
  • Anahtar Kelimeler: heat equation, Dirichlet problem, elliptic function, elliptic integral, green function, DIRICHLET PROBLEM, BOUNDARY, REGION
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

In this study, an alternative method is presented for the solution of two-dimensional heat equation in a square region. In this method, the solution function of the problem is based on the Green function, and therefore on elliptic functions. The numerical results have been computed for an application example and compared with the results of the well-known method of separation of variables and the finite elements method. The comparison study shows that the present method gives better results than those of the other methods. (C) 2007 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.