Effects of different discretisations of the Laplacian upon stochastic simulations of reaction-diffusion systems on both static and growing domains

DOI10.1016/j.cam.2021.113570zbMath1476.65162arXiv1911.11645OpenAlexW3154910192MaRDI QIDQ2029642

Bartosz J. Bartmanski, Ruth E. Baker

Publication date: 3 June 2021

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.11645

zbMATH Keywords

diffusionpattern formationreactionstochastic simulation

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Brownian motion (60J65) Fractional derivatives and integrals (26A33) Heat equation (35K05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Developmental biology, pattern formation (92C15) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Stochastic particle methods (65C35) Fractional partial differential equations (35R11) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) PDEs in connection with classical thermodynamics and heat transfer (35Q79) Fokker-Planck equations (35Q84) Pattern formations in context of PDEs (35B36) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75) Jump processes on general state spaces (60J76) Jump processes on discrete state spaces (60J74)

Uses Software

• MesoRD

Cites Work

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• Stochastic diffusion processes on Cartesian meshes
• Simulation of stochastic diffusion via first exit times
• Approximation and inference methods for stochastic biochemical kinetics—a tutorial review
• Analysis and Design of Jump Coefficients in Discrete Stochastic Diffusion Models
• The chemical basis of morphogenesis
• The Reaction-Diffusion Master Equation as an Asymptotic Approximation of Diffusion to a Small Target

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