Software and Data Associated with Paper "Data Assimilation in 2D Hyperbolic/Parabolic systems using stabilized explicit finite difference scheme run backward in time".

Images and Fortran codes used to generate results in the paper "Data Assimilation in 2D Hyperbolic/Parabolic systems using stabilized explicit finite difference scheme run backward in time" by Alfred Carasso. . In data assimilation one is given a proposed solution to a time-dependent partial differential equation at some time T and are asked to identify an initial condition at some earlier time 0 that evolves into the given solution at time T. In this paper an artificial example of a coupled system of three nonlinear partial differential equations generalizing 2D thermoelastic vibrations, is used to demonstrate the effectiveness, as well as the limitations, of a non-iterative direct procedure in data assimilation. Data assimilation is illustrated using 512 x 512 pixel images. Such images are associated with highly irregular non-smooth intensity data that severely challenge ill-posed reconstruction procedures.