Applications of finite and infinite Fourier series in heat processes with impulse data

Faydaoglu Ş., Yakhno V. G.

APPLIED MATHEMATICS AND COMPUTATION, cilt.218, sa.16, ss.8120-8130, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 218 Sayı: 16
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1016/j.amc.2011.08.093
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.8120-8130
  • Anahtar Kelimeler: Impulsive initial boundary value problem, Heat conduction equation, Eigenvalues, Eigenfunctions, Generalized solution, Regularized solution, COMPUTATIONS
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

Initial boundary value problems for the heat conduction equation with the constant and piecewise constant coefficients are considered in the paper. The Dirac delta function appears in the initial data. The considered problems are mathematical models of the temperature distribution arising from a pulse point heat source in homogeneous or two composite materials. The Fourier series expansion method is applied for solving these problems. The formal solutions are constructed in the form of the infinite series which are not classical functions. We show that these formal solutions are generalized functions (distributions). We prove that the partial sum of the constructed infinite series is a classical function which can be considered as a regularization of the generalized solution. The method of the computation of this regularized solution is suggested in the paper. The computational examples confirm the robustness of the proposed method. (C) 2011 Elsevier Inc. All rights reserved.