Numerical solution of generalized IHCP by discrete mollification

A numerical space marching algorithm based on discrete mollification and automatic iterative filtering by Generalized Cross Validation is applied to the solution of a generalized one-dimensional inverse heat conduction problem. No information about the noise is assumed. With data temperature and heat flux functions measured at a discrete set of points on the boundary x = 1, 0 less than or equal to t less than or equal to 1, the temperature and heat flux solution functions are approximately recovered in the unit square of the (x, t) plane, including its boundaries. Error bounds and numerical examples are provided.