A numerical study of inverse heat conduction problems

In this paper, two boundary element methods, a collocation method and a weighted method, are employed to solve a one-dimensional inverse heat conduction problem (IHCP). Inverse heat conduction problems are well known for being ill-posed. When numerical methods are directly applied on an IHCP, ill-conditioned linear systems will be involved. We show that the condition numbers for these systems increase as en where n is the number of the elements. We use a couple of Tikhonovʹs regularization methods to stabilize the matrix which is generated by the weighted method. An error bound for each method is analyzed. Finally, both methods are implemented and the result for the collocation method with the truncated singular value decomposition method is also shown in this article.