Approximation of backward heat conduction problem using Gaussian radial basis functions

S. Abbasbandy, B. Azarnavid, Ishak Hashim, A. Alsaedi

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this work an efficient numerical method is applied for investigation of the backward heat conduction problem in an unbounded region. The problem is ill-posed, in the sense that the solution if it exists, does not depend continuously on the data. The Gaussian radial basis functions are used for discretization of the problem. The presented method is reducing the problem to an interpolation problem which is more simple than the collocation type method. To regularize the resultant ill-conditioned linear system of equations, we apply successfully both the Tikhonov regularization technique and the L-curve method to obtain a stable numerical approximation to the solution. A new convenient and simply applicable method is derived. The stability and convergence of the proposed method are investigated. Two examples are presented to illustrate efficiency and accuracy of the proposed method.

Original languageEnglish
Pages (from-to)67-76
Number of pages10
JournalUPB Scientific Bulletin, Series A: Applied Mathematics and Physics
Volume76
Issue number4
Publication statusPublished - 2014

Fingerprint

Heat Conduction
Radial Functions
Heat conduction
conductive heat transfer
Basis Functions
collocation
Approximation
linear systems
approximation
interpolation
Linear systems
Numerical methods
Interpolation
curves
L-curve
Regularization Technique
Interpolation Problem
Tikhonov Regularization
Linear system of equations
Stability and Convergence

Keywords

  • Backward heat conduction problem
  • Gaussian radial basis function
  • ill-posed Problem

ASJC Scopus subject areas

  • Applied Mathematics
  • Physics and Astronomy(all)

Cite this

Approximation of backward heat conduction problem using Gaussian radial basis functions. / Abbasbandy, S.; Azarnavid, B.; Hashim, Ishak; Alsaedi, A.

In: UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, Vol. 76, No. 4, 2014, p. 67-76.

Research output: Contribution to journalArticle

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