An Algorithm for the Numerical Solutions of the Time-Space Fractional Reaction-Diffusion-Drift Equation

<p>The paper is devoted to the construction and program implementation of the computational algorithm for modeling a process of diffusion-drift nature based on the fractional diffusion approach. The mathematical model is formulated as an initial-boundary value problem for the time-space fractional diffusion-drift equation in a limited domain. Time and space fractional derivatives are considered in the sense of Caputo and Riemann – Liouville, respectively. A modified implicit finite-difference scheme is constructed. The concept of the considered mathematical problem provides an example of a deterministic model of the charging process of dielectric materials. An application program has been developed that implements the constructed numerical algorithm. The results were verified using the example of solving a test problem.</p>