February 14, 2017 --- Class 11 --- Higher Order Algorithms,
Sources of Numerical Analysis Code, Introduction to Mathematica
Activities:
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://physics.clarku.edu/sip/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 .
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
We looked briefly at the documentation for the GNU
Scientific Library and saw that a large number of algorithms
are available.
Introduction to Mathematica
A nine page Mathematica handout is available on the cluster at
~sg/mathematica_notes_with_graph.pdf
Over the next several classes we will go through the notes
and the examples it contains.
We covered Secs. A to E and will continue from there in the
next class.
A Mathematica notebook in ~sg/Documents/feb12_2017.nb records
what I did at the console.
~sg/Documents/feb16_2016.nb records what I did in a prior term.