# Partial Differential Equations- Scientific Computing TM

## ODE Project

As a preparation for this report you should make shure that you have worked through
the computer session E8.

The written report must include:
- A presentation of the problem you consider (e.g. the Akzo-Nobel system of chemical reations.)
- A short description of the dG(0) and the cG(1) methods for systems of ODE's.
- An explanation of the dual problem in your case.
- A short derivation of the a posteriori error estimate.
- An adaptive algorithm based on the posteriori error estimate (se for instance the smal note on adaptive
algorithms above)
- Implementation of an ode-solver based on the dG(0)-method including
adaptive time-stepping based on a posteriori
error estimation using duality. Consider also the cG(1)-method.
- Application of your solver to e.g. the Akzo-Nobel system of chemical reations. including both
and compute

corresponding stability factors for different outputs.