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Random walk algorithms for solving nonlinear chemotaxis problems

Author

Listed:
  • Sabelfeld Karl K.

    (Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Novosibirsk, Russia)

  • Bukhasheev Oleg

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

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.

Suggested Citation

  • Sabelfeld Karl K. & Bukhasheev Oleg, 2024. "Random walk algorithms for solving nonlinear chemotaxis problems," Monte Carlo Methods and Applications, De Gruyter, vol. 30(3), pages 235-248.
  • Handle: RePEc:bpj:mcmeap:v:30:y:2024:i:3:p:235-248:n:1003
    DOI: 10.1515/mcma-2024-2008
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