Construction of a discrete model of the diffusion equation in the state space based on a finite-difference scheme of the fourth order

The paper considers a one-dimensional diffusion model with boundary conditions of the first kind. A new discrete linear model in the state space obtained by discretization of the original continuous model on the basis of a finite-difference scheme of the fourth order of accuracy on the spatial variable is proposed. Various approaches to the identification of unknown parameters of the constructed model based on recurrent discrete filtering algorithms depending on the availability of a priori information are considered.