Numerical modeling of diffusion-wave polarization processes in ferroelectrics based on the time-fractional Landau–Khalatnikov equation

The paper deals with the fractional modification of the Landau–Khalatnikov model to describe diffusion-wave polarization processes in ferroelectrics. The problem is formalized as an initial-boundary value problem for a semilinear time-fractional partial differential equation. To solve the problem numerically, an implicit computational scheme was derived using the Grünwald–Letnikov derivative. The constructed numerical scheme was implemented in Matlab. The designed computer program was used to conduct simulations of the spatial-temporal polarization distributions and hysteresis loops for ferroelectrics with the second-order phase transitions. This approach allows one to provide more adequate modelling of polarization processes in complex physical systems due to the variation of regimes by means of changes in the dynamical dimension.