Time-Fractional Approach for Numerical Simulation of Temperature-Dependent Hysteresis in Ferroelectrics

The paper presents the time-fractional modification of the Landau - Ginzburg - Devonshire - Khalatnikov model to describe the dynamics of polarization switching and estimate temperature-dependent characteristics in ferroelectrics with the first order phase transition. The mathematical model is formal-ized by an initial-boundary value problem for a time-fractional cubic-quintic equation. To solve the problem numerically, we derived a computational scheme as a combination of an implicit finite-difference scheme and an iterative procedure. An application program was developed in Matlab to implement the designed computational algorithm. The special software allows one to predict and control the changes in polarization in polar dielectrics in different dynamical modes under variation of the order of the time-fractional derivative and time-dependent thermody-namic parameters. The results of computational experiments are discussed to assess temperature-dependent characteristics of polarization switching in BaTiO
3
ferroelectric crystals.