A new operational matrix method based on the Bernstein polynomials for solving the backward inverse heat conduction problems
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 1 April 2014
Issue publication date: 1 April 2014
Abstract
Purpose
The purpose of this paper is to introduce a novel approach based on the high-order matrix derivative of the Bernstein basis and collocation method and its employment to solve an interesting and ill-posed model in the heat conduction problems, homogeneous backward heat conduction problem (BHCP).
Design/methodology/approach
By using the properties of the Bernstein polynomials the problems are reduced to an ill-conditioned linear system of equations. To overcome the unstability of the standard methods for solving the system of equations an efficient technique based on the Tikhonov regularization technique with GCV function method is used for solving the ill-condition system.
Findings
The presented numerical results through table and figures demonstrate the validity and applicability and accuracy of the technique.
Originality/value
A novel method based on the high-order matrix derivative of the Bernstein basis and collocation method is developed and well-used to obtain the numerical solutions of an interesting and ill-posed model in heat conduction problems, homogeneous BHCP with high accuracy.
Keywords
Acknowledgements
The authors are very grateful to the reviewers of this paper for their helpful suggestions which have improved the paper very much.
Citation
Rostamy, D. and Karimi, K. (2014), "A new operational matrix method based on the Bernstein polynomials for solving the backward inverse heat conduction problems", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 24 No. 3, pp. 669-678. https://doi.org/10.1108/HFF-04-2012-0083
Publisher
:Emerald Group Publishing Limited
Copyright © 2014, Emerald Group Publishing Limited