An iterative algorithm for identifying heat source by using a DQ and a Lie-group method

We develop a novel yet simple iterative algorithm to solve a mixed-type inverse heat conduction problem, which is a combination of the Cauchy problem, the backward heat conduction problem (BHCP) and a heat source recovery problem. First, we transform the heat conduction equation into a new one, including a spring term and a damping term, which can raise the accuracy of numerical solution. Second, we use the differential quadrature method to semi-discretize the differential term, and then the group-preserving scheme leads to an accurate solution of the mixing Cauchy and BHCP. Third, with the aid of an overspecified right-end boundary condition, an iterative Lie-group adaptive method is developed to recover the space-dependent heat source function through a few iterations. The heat source term recovered is quite smooth, even the input data are polluted by a random noise, being large up to [GRAPHICS] . The accuracy and efficiency of the new methods are assessed by comparing the estimated results with exact solutions from several numerical examples.