Small toolbox for simulating reaction diffusion equations of the type
with the diffusion matrix
The space is discretized by finite differences and translated to a big ODE system which is solved using MATLABs ode15s
solver.
- Simulation of reaction diffusion equations in one or two spatial dimensions.
- Zeroflux and periodic boundary conditions.
- Easy model setup.
- Spatially dependend parameter possible.
- Import of D2D models (https://github.com/Data2Dynamics)
The model is specified in a .def
file in the subfolder /Models
of the current MATLAB working directory. The model file is structured like:
STATES
...
EQUATIONS
...
PARAMETERFIELDS
...
The section STATES
contains a list of the dynamical states u
together with a boolean variable specifying if the state is diffusive. The section EQUATIONS
contains a list with the ordinary differential equations (ODEs) defining the reaction part f(u(x,t))
of the reaction diffusion equation f(u(x,t))
. The section PARAMETERFIELDS
specifies all dynamical parameters which are spatially depend, i.e. k = k(x)
. See the example Diffusion_from_Source
for some use cases.