Numerical Solution of Some 2-Dimensional Direct and Inverse Heat Conduction Problems by Method of Fundamental Solutions

Document Type : Original Paper

Authors

1 PhD of Applied Mathematics- Department of Mathematics, Semnan University, Semnan, Iran.

2 Phd. Student- Department of Mathematics, Semnan University, Semnan, Iran.

3 Phd, Student- Department of Mathematics, Semnan University, Smnan, Iran

4 PhD of Pure Mathematics- Department of Mathematics, Semnan University, Semnan, Iran

Abstract

In this paper, a numerical method based on the method of fundamental solutions (MFS) is employed for solving some two dimensional direct and inverse heat conduction problems. Based on the fundamental solution to the heat equation and theoretical properties of these solutions, including linear independence and denseness, wih suitbale placement of source points, the MFS is introduced for solving two dimensional heat conduction problems. Since the resultant matrix of the MFS is ill-conditioned for solving direct and inverse problems, to regularize this matrix equation, we apply Tikhonov regularization technique, while the choice of the regularization parameter is based on L-curve critera to obtain a stable solution. Numerical results show the effectiveness and ability of the proposed method.

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References

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Journal of Advanced Mathematical Modeling
Volume 8, Issue 1
September 2018
Pages 65-86

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History

  • Receive Date: 21 January 2017
  • Revise Date: 05 August 2018
  • Accept Date: 13 August 2018

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