TY - JOUR

T1 - Random walk algorithms for solving nonlinear chemotaxis problems

AU - Sabelfeld, Karl K.

AU - Bukhasheev, Oleg

N1 - Support of the Russian Science Foundation under Grant 24-11-00107 is gratefully acknowledged.

PY - 2024/9/1

Y1 - 2024/9/1

N2 - 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.

AB - 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.

KW - Chemotaxis process

KW - Keller–Segel equation

KW - global random walk on grid

KW - randomized vector linear solver

KW - stochastic projection method

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85200321019&origin=inward&txGid=429bf044df98d2c1beb2d619f7948c9

UR - https://www.mendeley.com/catalogue/b67f3e9f-271d-3af3-a918-888154098954/

U2 - 10.1515/mcma-2024-2008

DO - 10.1515/mcma-2024-2008

M3 - Article

VL - 30

SP - 235

EP - 248

JO - Monte Carlo Methods and Applications

JF - Monte Carlo Methods and Applications

SN - 0929-9629

IS - 3

ER -