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

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  • Muhammad Arghand
  • Majid Amirfakhrian

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.

Suggested Citation

  • Muhammad Arghand & Majid Amirfakhrian, 2015. "A Meshless Method Based on the Fundamental Solution and Radial Basis Function for Solving an Inverse Heat Conduction Problem," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-8, April.
    • Handle: RePEc:hin:jnlamp:256726
    DOI: 10.1155/2015/256726
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