September 27, 2007 --- Class 10 --- Sources of Numerical Analysis Code,
Higher Order Algorithms
Activities:
Sources of Numerical Analysis Code
So far, we have built our own codes from scratch; however,
you will probably find it very useful to make use of
standard codes that are already debugged. Two good sources
of code for numerical analysis are the book "Numerical
Recipes" (which is recommended for this course) and the GNU
scientific library.
GNU scientific library can be found at:
http://www.gnu.org/software/gsl
Code from Numerical Recipes is not so freely available. But
older versions of the text and source can be found here:
http://www.nrbook.com
The latest version of the book and information about electronic
access are here:
http://www.nr.com
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 5A of Chapter 5.
On page 128. There are two typos in the book regarding
the 4th order R-K algorithm. In Eq. (5.59a), the right-hand-
side should be multiplied by Delta t. In Eq. (5.59b), k_3x
on the RHS should be k_3v
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