A Meshless Method Based on the Fundamental Solution and Radial Basis Function for Solving an Inverse Heat Conduction Problem. (14th April 2015)

• Record Type: Journal Article
• Authors: Arghand, Muhammad; Amirfakhrian, Majid
• Other Names: Punjabi Alkesh Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2015(2015)
• Publication Date: 2015-04-14
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2015/256726
• Languages: English
• ISSNs: 1687-9120

Abstract

Abstract : 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.