Re: NDSolve-memory

*To*: mathgroup at smc.vnet.net*Subject*: [mg32040] Re: NDSolve-memory*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Thu, 20 Dec 2001 03:42:02 -0500 (EST)*Organization*: Universitaet Leipzig*References*: <9vpnff$c9r$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi, my package with Runge-Kutta solvers http://phong.informatik.uni-leipzig.de/~kuska/visualsupp/RungeKuttaNDSolve.m has a RKReturn option. With RKReturn->RKEndPoint no interpolation is generated and only the end point is returned. If you set RKReturn-> RKInterpolation an interpolation function is generated.RKReturn->RKPoincareSection make a Poincare section on the hypersurface that is given by PSHyperplane option. The solvers expect a system of first order equations. The equations must be autonom. The Runge-Kutta methods are for non-stiff and middle-stiff problems. With the Method option you can select methods of order 3-8 and atleast the higher order metthods should work with middle stiff problems. The RKReturn->RKEndPoint option should solve your problem. Regards Jens Pieter-Jan.DeSmet at fys.kuleuven.ac.be wrote: > > Dear readers, > > I have a system of differential equations > > F( y(t) ,y'(t) ,t )=0, with initial condition y(0) = y0. > > Here y(t) is a vector-valued function, let us denote the dimension of > this vector by n. When I solve this system in Mathematica with NDSolve, > the program uses too much memory and crashes if n is too big. > (In my case this happens when n = 6). > > I am however only interested in the value of y at t=1 ( y(1) ). So, I think > that Mathematica can be more memory efficient if it throws away all > previous values of y(t) it does not need anymore in its difference scheme. Is > there a method to impose this? Of course, the result of NDSolve would not give > an InterpolatingFunction object any more. > > Other suggestions to reduce the needed memory are also appreciated. Lowering > PrecisionGoal and AccuracyGoal does not seem have much effect on the memory. > > Pieter-Jan De Smet