February 18, 2013 --- Class 11 --- Higher Order Algorithms,
Introduction to Mathematica
Activities:
Homework
I discussed what I was looking for on the homework and
some of the challenges in the second problem. In general,
performance on the homework was excellent. If you have any
questions, please come to see me. It is important to master
the skills required to solve these initial problems.
Higher order algorithms
We talked about several algorithms including leap frog
Adams-Bashforth and Runge-Kutta. Euler-Richardson is
basically the 2nd order Runge-Kutta algorithm. We also
talked about the 4th order Runge-Kutta algorithm. Many of
these algorithms are presented in Appendix 3A of Chapter 3.,
starting on page 74. There are two typos in the book regarding
the 4th order R-K algorithm. In Eq. (3.61g), the right-hand-
side should be multiplied by Delta t. In Eq. (3.61h), k_3x
on the RHS should be k_3v. Corrections to the textbook can
be found at http://sip.clarku.edu/3e/updates.html .
You may also find more about these algorithms in "Numerical
Analysis" by Burden and Faires, or "Numerical Recipes" by
Press et al.
My notes can be found at
http://www.physics.indiana.edu/~sg/p609/ode_algorithms.pdf
or on the cluster in ~sg/ode_algorithms.pdf .
Introduction to Mathematica
An eight page handout on Mathematica is available at
~sg/mathematica_notes_sg.pdf
Over the next several classes we will go through the notes
and the examples it contains.
There is a wide variation among class members' familiarity
with Mathematica. We covered Secs. A and B and will continue
from there.