Re: ODE solvers in Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg33227] Re: ODE solvers in Mathematica
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Sat, 9 Mar 2002 18:05:10 -0500 (EST)
- Organization: Universitaet Leipzig
- References: <a6chi9$dqt$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
- Sender: owner-wri-mathgroup at wolfram.com
Hi, AFAIK NDSolve[] use a Adams-Bashford/Adams-Multon predictor corrector method, if the system is stiff it switchs to the classical Gear algorithm. When the Method is set to Runge-Kutta it uses probably the classicak Runge-Kutta formula. I have an implementation of the most recent enbedded Runge-Kutta Methods in: http://phong.informatik.uni-leipzig.de/~kuska/visualsupp/RungeKuttaNDSolve.m including the Dormand/Price 5(4) method and the 8(7) method. The most methods have a continuous output and can compute Poincare sections. All methods are written for systems of first order. The RADAU code of Ernst Hairer is for algebo equations and Mathematica can't solve mixed systems of differntial and algebraic equations. You can use the symbolic power to eliminate the algebraic equations. I have a implentation of Ernst Hairer's symmetric projection algorithm espcial for symplectic integration http://phong.informatik.uni-leipzig.de/~kuska/visualsupp/ManifoldNDSolve.m that is impressive robust and should work well for index 1 algebros. Regards Jens Higinio Ramos wrote: > > I'm interested in comparing an ODE solver with the standard ones: > DOPRI,RADAU,HAIRER, etc. > Does anyone know if they are implemented in Mathematica? > Thanks in advance. > Higinio Ramos