Mathematical model of polarization switching based on the generalised Landau–Khalatnikov–Tani equation: numerical implementation

<p>The paper presents a review of existing mathematical models describing the dynamics of polarization changes in ferroelectrics based on Landau's thermodynamic theory. Particular attention is given to the generalised Landau–Khalatnikov–Tani model, which accounts for inertial effects and enables the description of hysteresis phenomena. The model is formulated as an initial-boundary value problem for a hyperbolic-type partial differential equation. An implicit finite-difference scheme is constructed for the numerical solution of the problem. Results of computational experiments are presented, demonstrating polarization switching and the formation of dielectric hysteresis in ferroelectric materials undergoing first-order phase transitions.</p>