FitzHugh-Nagumo Reaction-Diffusion Equation Solver

Motivation

This projects aims at providing a solver for the FitzHugh-Nagumo Reaction-Diffusion nonlinear PDE, as well as code which can extract the PDE's parameters.

This code was created as an assignment for the Modelling & Scientific Computing module, at the EPSRC CDT in Sustainable Approached to Biomedical Sciences: Responsible and Reproducible Research - SABS R3

Installation

In order to install the packaged, the user will require the presence of Python3 and the pip3 installer.

For installation on Linux or OSX, use the following commands. This will create an environment and automatically install all the requirements.

python3 -m venv env
source env/bin/activate
pip install -e .

Usage

In order to run the solver, type the following commands int the activated python environment. For a simple solver type in the first command, for a fourier transform based solver ued the second command, while for the moldel fitting function type in the second command.

python PDE_solver.py

python solver_using_fourier_transforms.py

python model_fitting.py

The user should know that, in it's current format, the codes are not completely operational. The PDE-solver is currently fails to capture the analytical solution. The solver-using-fourier-transforms currently is operational, however it still has certain issues. The model-fitting script is operational, however it still suffers from dimensionality issues due to incompatibilities with the previous two solvers. In previous tests, however, it proved to be working.

Contributing

Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change.

Please make sure to update tests as appropriate.

License

BSD 3-Clause License © Alister Dale-Evans, Andrei Roibu, Pavan Chaggar, Rebecca Rumney

References

In the creation of this code, material was used from the following papers:

@article{parand2017numerical,
title={A numerical method to solve the 1D and the 2D reaction diffusion equation based on Bessel functions and Jacobian free Newton-Krylov subspace methods},
author={Parand, K and Nikarya, M},
journal={The European Physical Journal Plus},
volume={132},
number={11},
pages={496},
year={2017},
publisher={Springer}
}

@article{10.2307/3212689,
    ISSN = {00219002},
    URL = {http://www.jstor.org/stable/3212689},
    author = {Jenö Gazdag and José Canosa},
    journal = {Journal of Applied Probability},
    number = {3},
    pages = {445--457},
    publisher = {Applied Probability Trust},
    title = {Numerical Solution of Fisher's Equation},
    volume = {11},
    year = {1974}
    }

Credits

The team would like to express their gratitude to Martin Robinson and Aleksandra Ardaseva for their help and support during the development of this code.

Build status

Basic tests have been written for testing the code. They can be found in the test_iterative_PDE.py file, and can be ran using the command:

python test_iterative_PDE.py

More complex tests will be added as the code is further developed.