Computational techniques for time-fractional modeling of thermal wave propagation in ferroelectrics

Abstract

The paper proposes a time-fractional modified model of thermal wave propagation in ferroelectrics. To solve the initial-boundary value problem for a partial differential equation numerically, an implicit computational scheme was derived using a finite-difference approximation of the time-fractional Caputo derivative. The constructed numerical scheme was implemented in Matlab. The designed computer program was used to conduct simulations of the space-time thermal distribution in typical ferroelectrics associated with the dynamical pyroelectric measurements. This approach allows us to provide more adequate modelling of heat conductivity processes in complex physical systems due to the variation of regimes by means of changes in the fractal dynamical dimension.