Iterative solution of a retrospective inverse problem of heat conduction with inhomogeneous Dirichlet boundary conditions

We consider a retrospective inverse problem of heat conduction with non-stationary inhomogeneous Dirichlet boundary conditions. It is approximated by the Crank—Nicolson difference scheme, which has the second order of approximation both in the spatial variable and in time. To determine the solution of the resulting system of linear algebraic equations, it is proposed to use the iterative method of conjugate gradients. Examples are given of restoring smooth, nonsmooth, and discontinuous initial conditions, including the introduction of «noise» characteristic of additional conditions of inverse problems and its smoothing using the Savitsky—Golay filter.