A nonlinear inverse heat transfer problem

AbstractThis paper deals, in the one-dimensional case, with an inverse problem for the heat equation. Such a problem is a two points initial-boundary value problem with boundary conditions correctly posed only on one of the extremities, the missing boundary conditions being replaced by a measurement of the temperature in an inner point of the space domain.The result is obtained developing an original Bellman's idea: “the differential quadrature method” which is here developed in the framework of a decomposition of domains technique