Modeling of Nonstationary Distributed Processes on the Basis of Multidimensional Time Series

A method for identifying the equations of mathematical physics describing the dynamics of spatially-distributed processes on the basis of experimental multidimensional time series is proposed. The method includes the LSM (Least square method) estimates of the parameters of multidimensional autoregression and the construction of versions of systems of algebraic equations connecting the estimates of autoregression and the parameters of the corresponding differential equations. The system of algebraic equations satisfied by the obtained estimates determines the structure of the model and the corresponding values of the parameters of differential equation. A numerical example of identifying the processes of changing the temperature of atmospheric air is given.