Lattice Boltzmann method for the multiterm time-fractional mixed diffusion and diffusion-wave equations
Phys. Rev. E 112, 045308 – Published 7 October, 2025
DOI: https://doi.org/10.1103/m2yd-yxyf
Abstract
In this paper, a unified lattice Boltzmann model is developed to solve the multiterm time-fractional mixed diffusion and diffusion-wave equations. To obtain the standard form of the equation, the Caputo derivative terms are approximated using numerical differentiation and composite integration rules. By selecting appropriate auxiliary distribution functions and equilibrium distribution functions, the macroscopic equation is properly recovered. A series of numerical simulations are performed, demonstrating that the results of the proposed method agree well with the analytical solutions. The efficiency of the proposed lattice Boltzmann model is thus validated.
