Cheg 258 - Lecture Notes - April 23, 1999
Announcements
- Example 34, linked into today's notes, is a good example of how to use
the shooting method to solve boundary value problems. You will want to look
at it when you solve problem 30.
- Don't panic over all the fluid mechanics included in the description of
problem 30. You can actually pretty much ignore the whole first page, but I
thought you might like to know the physical basis of the ODE you are to solve...
Class notes
Scanned Notes
The main points of the lecture were
- Adaptive Step Size Algorithms
Goals:
After this class you should be able to:
- Write an integration algorithm which adapts the step size to the accuracy
of the integration process.
Reading
- The class notes and Ch. 8 of Kahaner.
Questions of the Day
- In the Fehlberg Runge-Kutta approach the two integration estimates have
global errors of O(h^4) and O(h^5). If the set tolerance is t, how do you calculate
the step size?
- How does this answer change if the equation is very stiff?
Matlab Example Codes
example 33
-
ode23.m
-
example 34
David.T.Leighton.1@nd.edu