### 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 language | English |
---|---|

Pages (from-to) | 67-76 |

Number of pages | 10 |

Journal | UPB Scientific Bulletin, Series A: Applied Mathematics and Physics |

Volume | 76 |

Issue number | 4 |

Publication status | Published - 2014 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics
- Physics and Astronomy(all)

### Cite this

*UPB Scientific Bulletin, Series A: Applied Mathematics and Physics*,

*76*(4), 67-76.

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

Research output: Contribution to journal › Article

*UPB Scientific Bulletin, Series A: Applied Mathematics and Physics*, vol. 76, no. 4, pp. 67-76.

}

TY - JOUR

T1 - Approximation of backward heat conduction problem using Gaussian radial basis functions

AU - Abbasbandy, S.

AU - Azarnavid, B.

AU - Hashim, Ishak

AU - Alsaedi, A.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Backward heat conduction problem

KW - Gaussian radial basis function

KW - ill-posed Problem

UR - http://www.scopus.com/inward/record.url?scp=84944681232&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84944681232&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84944681232

VL - 76

SP - 67

EP - 76

JO - UPB Scientific Bulletin, Series A: Applied Mathematics and Physics

JF - UPB Scientific Bulletin, Series A: Applied Mathematics and Physics

SN - 1223-7027

IS - 4

ER -