An iterative boundary element method for solving the backward heat conduction problem using an elliptic approximation

In this paper a new numerical method which does not require a regularization parameter is developed for solving the backward heat conduction problem (BHCP). The inverse and ill-posed BHCP for the heat equation is approximated with a convergent sequence of elliptic Cauchy problems for which the stable algorithm of the Kozlov et al. [1] type is accommodated. Further, a boundary element method (BEM) is developed for obtaining a stable solution of the BHCP.

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