Numerical Computation Based on the Method of Fundamental Solutions for a Cauchy Problem of Heat Equation

Ruihua Cao^1,

¹School of Mathematics and Computer science, Shanxi Normal University, Linfen, China

Cite this paper:
Ruihua Cao. Numerical Computation Based on the Method of Fundamental Solutions for a Cauchy Problem of Heat Equation. Turkish Journal of Analysis and Number Theory. 2014; 2(3):70-74. doi: 10.12691/tjant-2-3-3

Abstract

In this note, a boundary integral equation method coupled with the method of fundamental solutions for solving an inverse heat conduction problem is considered. The Tikhonov regularization method is employed for solving this system of equations. Determination of regularization parameter is based on GCV criterion. To illustrate our main results, some numerical examples are given.

Keywords:
inverse problem of the heat equation method of fundamental solutions integral equation method

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	L. Ling, T. Takeuchi. Boundary control for inverse Cauchy problems of the Laplace equations. CMES Comput Model Eng Sci, 2008, Vol. 29, No. 1, pp. 45-54.
[2]	M. C. Flemings. Solidification processing. McGraw-Hill, New York, 1974.
[3]	D. A. Porter, K. E. Easteling. Phase Transformations in Metals and Alloys. Chapman Hall, London, 1981.
[4]	D. Lesnic, L Elliott, D. B. Ingham. Application of the boundary element method to inverse heat conduction problems. International Communications in Heat and Mass Transfer, 1996 Vol. 39, No. 7, PP. 1503-1517.
[5]	L Guo, D. Murio. A mollified space-marching finite-difference algorithm for the two-dimensional inverse heat conduction problem with slab symmetry. Inverse problem, 1991, Vol. 7, No. 2, PP. 247-259.
[6]	T. R. Hsu, N. S. Sun, G.G. Chen, Z. L. Gong. Finite element formulation for two-dimensional inverse heat conduction analysis. Journal of Heat Transfer, 1992, Vol. 114. No. 3, PP. 553-557.
[7]	T. Wei, Y. C. Hon. A fundamental solution method for inverse heat conduction problem. Engineering analysis with boundary elements, 2004, Vol. 28, No. 5, pp. 489-495.
[8]	Y. C. Hon, T. Wei. The method of fundamental solution for solving multidimensional inverse heat conduction problems. CMES Compt. Model. Eng. Sci, 2005, Vol. 7, No. 2, pp. 119-132.
[9]	A. N. Tikhonov, V. Y. Arsenin. On the solution of ill-posed problems. John Wiley and Sons, New York, 1977.
[10]	T. Wei, Y. C. Hon, L. Ling. Method of fundamental solutions with regularization techniques for Cauchy problems of elliptic operators. Engineering Analysis with Boundary Elements, 2007, Vol. 31, No. 4, pp. 373-385.
[11]	P. C. Hansen. Regularization Tools: a Matlab package for analysis and solution of discrete of ill-posed problems. Numerical Algorithms, 1994, Vol. 6, No. 1-2, PP. 1-35.