The method of fundamental solutions for the backward heat conduction problem

In this article a meshless numerical scheme for solving the backward heat conduction problem (BHCP) is proposed. The numerical solution is developed by using the fundamental solution of the heat equation as a basis function. The standard Tikhonov regularization technique and the L-curve method are adopted for solving the resultant ill-conditioned system of linear algebraic equations. The convergence and the stability of the method are investigated for a severe test example, hence revealing the computational performance and limitations of the method proposed. Numerical results are presented for bo th the one-dimensional and the two-dimensional backward heat conduction problems.