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Advances in Mathematical Physics
Volume 2015, Article ID 256726, 8 pages
Research Article

A Meshless Method Based on the Fundamental Solution and Radial Basis Function for Solving an Inverse Heat Conduction Problem

Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

Received 25 November 2014; Accepted 11 March 2015

Academic Editor: Alkesh Punjabi

Copyright © 2015 Muhammad Arghand and Majid Amirfakhrian. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose a new meshless method to solve a backward inverse heat conduction problem. The numerical scheme, based on the fundamental solution of the heat equation and radial basis functions (RBFs), is used to obtain a numerical solution. Since the coefficients matrix is ill-conditioned, the Tikhonov regularization (TR) method is employed to solve the resulted system of linear equations. Also, the generalized cross-validation (GCV) criterion is applied to choose a regularization parameter. A test problem demonstrates the stability, accuracy, and efficiency of the proposed method.