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

摘要

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 Kozlovet al.1 type is accommodated. Further, a boundary element method (BEM) is developed for obtaining a stable solution of the BHCP.