Matematik och Datavetenskap, Chalmers Tekniska Högskola och Göteborgs Universitet
Task:
(a) Write a matlab program that solves the initial value problem for a general system of ordinary differential equations. You will do this step by step during the weekly work assignments.
(b) Choose an application from the real world that can be modelled as such a system. You may choose from the following topics: mechanical systems, population dynamics, chemical reaction kinetics, molecule dynamics, economics, electrical circuits, or some other topic that you find interesting.
For your application you should consider several of the following aspects:
mathematical
derive the equations
find stationary points
linearize the equations
stability
long time behavior
periodic solutions
computational
solve intial value problem
plot solution curves, phase portrait
accuracy, compare with exact solution if available
compute stationary points by Newton's method
solve linearized equations
Report:
Write a report containing the following
title, authors, abstract, introduction, conclusion, references.
Present the report in front of your group during week 7.
You may work in groups of two or three, but each student must take an active part in the presentation.
/stig