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I like the NR book but its code, whether in Basic, C, or Fortran is best avoided unless you've no idea what you're doing. For the numerical solution of ode/dae's try http://www.unige.ch/math/folks/hairer/software.html and consult, or - heaven's forbid -, study Hairer's books. Good Luck, Gerry T. -----Original Message----- From: Van Snyder <[log in to unmask]> To: [log in to unmask] <[log in to unmask]> Date: Wednesday, September 27, 2000 1:18 PM Subject: Runge-Kutta > >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. > > > > %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%