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Modelling and Data Analysis
2025. Vol. 15, no. 3, 131–147
doi:10.17759/mda.2025150308
ISSN: 2219-3758 / 2311-9454 (online)

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

 
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Abstract

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.

General Information

Keywords: Landau – Khalatnikov – Tani equation, implicit finite-difference scheme, ferroelectric, polarization hysteresis, computational experiment

Journal rubric: Numerical Methods

Article type: scientific article

DOI: https://doi.org/10.17759/mda.2025150308

Received 03.08.2025

Revised 13.08.2025

Accepted

Published

For citation: Moroz, L.I., Doroshkov, O.S. (2025). Mathematical model of polarization switching based on the generalised Landau–Khalatnikov–Tani equation: numerical implementation. Modelling and Data Analysis, 15(3), 131–147. (In Russ.). https://doi.org/10.17759/mda.2025150308

© Moroz L.I., Doroshkov O.S., 2025

License: CC BY-NC 4.0

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Information About the Authors

Lubove I. Moroz, Candidate of Science (Physics and Matematics), Laboratory for Modeling Complex Physical and Biological Systems, Amur State University, Blagoveshchensk, Russian Federation, ORCID: https://orcid.org/0000-0003-4450-3200, e-mail: lubovep@mail.ru

Oleg S. Doroshkov, Bachelor of Science in Applied Mathematics and Computer Science, Institute of Computer Science and Engineering, Amur State University, Blagoveshchensk, Russian Federation, e-mail: oleg2003dos@gmail.com

Contribution of the authors

Moroz L.I. – research concept, annotation, manuscript writing, supervision of the study. 

Doroshkov O.S. – application of numerical methods, conducting experiments, programming, data collection and analysis, visualization of results. 

All authors participated in the discussion of results and approved the final manuscript text.

Conflict of interest

The authors declare no conflict of interest.

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