Vrabel Imrich asked:
> does anybody know, please, where may I find a fifth or higher
> order Runge-Kutta algorithm(s).
and Loren Meissner suggested:
> See "Numerical Recipes in Fortran, Second Edition," 1992 (ISBN
> 0-521-43064-X) page704-715.
> But if you need something better than 4th order Runge-Kutta, you probably
> want to consider Bulirsch-Stoer or predictor-corrector methods (see the
> discussion at the beginning of the chapter in Numerical Recipes, especially
> p 703).
and then quoted:
> "Runge-Kutta is what you use when (1) you don't know any better, or (ii) you
> have an intransigent problem where Bulirsch-Stoer is failing, or (iii) you
> have a trivial problem where computational efficiency is of no concern."
1. Numerical Recipes is not a superior reference for numerical methods.
I have received several testimonials about defects therein. There are
parts of it that do work. See http://math.jpl.nasa.gov/nr
2. Bulirsch-Stoer is not a superior method. Predictor-corrector methods
are superior, if evaluation of the derivative is expensive.
3. Runge-Kutta has superior error properties, and is faster than predictor-
corrector if (1) the system is first order and (2) the derivatives are
cheap to compute. It is difficult to construct a Runge-Kutta formula that
directly integrates systems of equations having order higher than first.
It is not difficult to construct Adams-type methods that integrate systems
of equations having order higher than first, but it is unusual to find
an implementation that actually does it. Integrating systems having
order higher than one directly results in better error propogation
characteristics, and substantially (150%) faster solution.
For good codes, look first at http://netlib.org or http://gams.nist.gov.
Use Numerical Recipes only as a last resort.
--
What fraction of Americans believe | Van Snyder
Wrestling is real and NASA is fake? | [log in to unmask]
Any alleged opinions are my own and have not been approved or disapproved
by JPL, CalTech, NASA, Dan Goldin, Bill Clinton, the Pope, or anybody else.
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