Abstract: In the paper, we apply stochastic projection methods to calculate solutions of two chemotaxis models, a two-component Keller-Segel model and a three-component reaction-diffusion model. Both models are described by non-linear drift-diffusion-reaction systems. To solve these problems, we use splitting of the equation in time where at each small time step one solves a linear diffusion-reaction equation and passes the calculated solution to thedrift-diffusion-reaction equation that is solved on the next time step. We transform the reaction-diffusion system into a matrix form using a finite-difference approximation of the equations of the system. The resulting systems of linear algebraic equations are solved by a stochastic projection method with refinement. We test the time-iterative algorithm and the projection method with refinement on the minimal non-local Keller-Segel model with a known exact solution and apply these algorithms to solve the three-component reaction-diffusion model. It is shown that the iterative refinement algorithm makes it possible to increase the accuracy of solution of the entire system describing the chemotaxis process. Results obtained by the stochastic projection method with refinement are compared also with the results calculated by using the LAPACKE dgesv subroutine that show a good agreement.

Cite: Sabelfed K.K. , Kireeva A.E.
Stochastic projection method with refinement for modelling three-component chemotaxis processes
Partial Differential Equations and Applications. 2025.

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Submitted:

Feb 4, 2025

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