pauljxtan / odeint

An easily extensible ODE integrator

odeint

An easily extensible ODE integrator in C. Mainly a learning project for practicing with pointers, memory allocation and data structures; not really optimized for efficiency, but being C, is still fairly fast.

Documented for Doxygen in Qt style -- pages hosted at http://pauljxtan.github.io/odeint.

Currently implemented

Method (struct_name):

• 4th-order Runge-Kutta (rk4)
• Forward Euler (fweuler)
• Bulirsch-Stoer (bulsto)

System (function_name):

• Brusselator (brusselator)
• Chen system (chen)
• Damped spring (damped_spring)
• Double pendulum (double_pendulum)
• Duffing equation (duffing)
• Lorenz attractor (lorenz)
• Lotka-Volterra equations (lotka)
• Parrot system {Borelli & Coleman 1987} (parrot)
• Rossler system (rossler)
• Symmetric top (symmetric_top)
• Van der pol oscillator (vanderpol)
• Van der pol oscillator 2-D (vanderpol2d)

Quick start

Integrate the Lorenz attractor using RK4, with the following parameters:

• time-step size : 0.01
• initial time : 0.0
• initial state : x=0.01, y=0.01, z=0.01
• number of steps : 10000
• verbose mode : yes (might be a big bottleneck for program speed)
• print parameters: yes
• write to file : yes [filename="lorenz.dat"]

$ ./src/integrate rk4 lorenz -d 0.01 -t 0.0 -x 0.01 -x 0.01 -x 0.01 -n 10000 -v -y -w

Then one could visualize the results with gnuplot, for example: gnuplot> splot "lorenz.dat" using 2:3:4 with lines

(To browse all available systems, run ./integrate without arguments.)

Real-time plotting

We can plot the time-series for each variable in real-time by piping the integration data into the Python plotting script, e.g.:

$ ./integrate rk4 lotka -d 0.05 -t 0.0 -x 10.0 -x 5.0 -n 1000 -v | ./plot_stdin_timeseries.py

or from a data file:

$ ./plot_stdin_timeseries.py < lotka.dat

Adding systems

1. Declare the function in ./include/eoms.h
2. Define the constants in ./include/eoms.h
3. Add the function to the function table and function list in ./src/eoms.c
4. Define the function in ./src/eoms.c
5. All set!

GUI

A Tkinter-based GUI is located at ./python/odeintgui.py. Requires Python and matplotlib 1.0.0+ with the Tk backend. Try it out!

Java version

A Java object-oriented implementation may be found in ./java/. Working, but still under heavy construction.

To-do

• Add "kwargs" functionality for passing additional parameters (e.g. constants) to integrator
• Adaptive methods