Random walk algorithms for solving nonlinear chemotaxis problems

Author:

Sabelfeld Karl K.1ORCID,Bukhasheev Oleg2

Affiliation:

1. Institute of Computational Mathematics and Mathematical Geophysics , Russian Academy of Sciences , Novosibirsk , Russia

2. Novosibirsk State University , Pirogova str. 2, 630090 Novosibirsk , Russia

Abstract

Abstract Random walk based stochastic simulation methods for solving a nonlinear system of coupled transient diffusion and drift-diffusion equations governing a two-component chemotaxis process are developed. The nonlinear system is solved by linearization, the system is evolved in time, by small time steps, where on each step a linear system of equations is solved by using the solution from the previous time step. Three different stochastic algorithms are suggested, (1) the global random walk on grid (GRWG), (2) a randomized vector algorithm (RVA) based on a special transformation of the original matrix to a stochastic matrix, and (3) a stochastic projection algorithm (SPA). To get high precision results, these methods are combined with an iterative refinement method.

Funder

Russian Science Foundation

Publisher

Walter de Gruyter GmbH

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