A script to generate code and symbolic expressions for high order explicit or implicit BDF methods using computational algebra (sympy).

The BDF methods are a widely used family of initial value ordinary differential equation solvers. In normal usage only the implicit methods of this family are useful, but there are certain cases when the explicit methods are useful.

The higher order explicit BDF methods are somewhat difficult to calculate by hand, due to the sheer volume of algebra required, hence the requirement for this script.

You will need python (tested with python 2.76 but hopefully compatible with python 3+ as well) and sympy (tested with version 0.7.4.1) installed. On a Debian-based machine these can be installed with the command

sudo apt-get install python python-sympy

Then to generate, for example, the 3rd order explicit method simply run

./generate-bdf-method.py --order 3 --explicit true

Additional help is available with the -h flag.

Automatic tests are done using nose. Install nose with the command

sudo apt-get install python-nose

Then run all tests with

nosetests generate-bdf-method.py