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Re: ODE solvers in Mathematica

  • To: mathgroup at
  • Subject: [mg33227] Re: ODE solvers in Mathematica
  • From: Jens-Peer Kuska <kuska at>
  • Date: Sat, 9 Mar 2002 18:05:10 -0500 (EST)
  • Organization: Universitaet Leipzig
  • References: <a6chi9$dqt$>
  • Reply-to: kuska at
  • Sender: owner-wri-mathgroup at


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:

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

that is impressive robust and should work well for index 1 algebros.


Higinio Ramos wrote:
> I'm interested in comparing an ODE solver with the standard ones:
> Does anyone know if they are implemented in Mathematica?
> Thanks in advance.
> Higinio Ramos

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