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