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Unstructured Reaction-Diffusion Master Equation

URDME is a general software framework for modeling and simulation of stochastic reaction-diffusion processes on arbitrary meshes. URDME emphasizes modularity in order to be useful both as a simulation tool and as a framework for development of stochastic simulation algorithms.

URDME 1.4. Copyright 2008--2020

See the file AUTHORS for a complete list of authors.

Quick Start

Download the latest stable release and unpack it, alternatively clone the repository (requires a git client),

$ git clone

To start using URDME under Matlab, navigate to the file startup.m,

>> startup

To run a simple 1D model,

>> cd examples/annihilation
>> annihilation_run

For further instructions, examples and tutorials, consult the software manual,


System requirements and software dependencies

See the file VERSION for a complete list.

Licence: GPL 3

See the file LICENCE for the full statement.

Citing URDME:

URDME is a research software and correctly citing it is important to the maintainers.

  • The software package; B. Drawert, S. Engblom and A. Hellander: "URDME: A modular framework for stochastic simulation of reaction-transport processes in complex geometries", BMC Systems Biology 6(76):1--17 (2012) (doi)

  • The underlying numerical modeling; S. Engblom, L. Ferm, A. Hellander and P. Lötstedt: "Simulation of stochastic reaction--diffusion processes on unstructured meshes", SIAM J. Scientific. Comp. 31(3):1774--1797 (2009) (doi)

  • The subdiffusion workflow; S. Engblom, P. Lötstedt and L. Meinecke: "Mesoscopic Modeling of Random Walk and Reactions in Crowded Media, Phys. Rev. E 98(3):033304 (2018) (doi)

  • The neuron workflow; P. Bauer, S. Engblom, S. Mikulovic and A. Senek: "Multiscale modelling via split-step methods in neural firing", Math. Comput. Model. Dyn. Syst. 24(4):409--425 (2018) (doi)

  • The DLCM workflow; S. Engblom, D. B. Wilson and R. E. Baker: "Scalable population-level modelling of biological cells incorporating mechanics and kinetics in continuous time", Roy. Soc. Open Sci. 5(8) (2018) (doi), and related, S.Engblom: "Stochastic simulation of pattern formation in growing tissue: a multilevel approach", Bull. Math. Biol. 81:3010--3023 (2019) (doi)

  • The AEM solver; P. Bauer and S. Engblom: "Sensitivity estimation and inverse problems in spatial stochastic models of chemical kinetics", pp. 519--527 in A. Abdulle, S. Deparis, D. Kressner, F. Nobile and M. Picasso (editors): "Numerical Mathematics and Advanced Applications: ENUMATH 2013", vol 103 of Lecture Notes in Computational Science and Engineering, Springer (2015) (doi)

  • The UDS solver implements the first order method described in S. Engblom: "Computing the Moments of High Dimensional Solutions of the Master Equation" Appl. Math. Comput. 18(2):498--515 (2006) (doi)


Stochastic reaction-diffusion simulation on unstructured meshes.



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