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Re: NDSolve precision and velocity problem

• To: mathgroup at smc.vnet.net
• Subject: [mg91312] Re: NDSolve precision and velocity problem
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Fri, 15 Aug 2008 06:52:44 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <g81378$o$1@smc.vnet.net>

Joerg Schaber wrote:

> I have an ODE system that takes lots of time to solve with NDSolve 
> (several minutes),
> whereas the same system with the FORTRAN solver LSODA
> solves the problem in an second.
> When I decrease the precision, e.g. AccuracyGoal->6, NDSolve crashes. It 
> often crashes, because it finds complex values in a less-than-comparison.
> 
> Maybe it's a method problem.
> How do I tell NDSolve, to use the same methods as the LSODEA solver?

If by the above you mean using either Adams or Backward Differentiation 
Formula (BDF) methods [1], for nonstiff or stiff cases, respectively, 
you can use the option *Method*.

The following might be worth reading (or at least browsing): [2, 3, 4]

Regards,
- Jean-Marc

[1] "LSODE", _Serial Fortran Solvers for ODE Initial Value Problems_,
https://computation.llnl.gov/casc/odepack/odepack_home.html

[2] _IDA Method for NDSolve_,
http://reference.wolfram.com/mathematica/tutorial/NDSolveIDAMethod.html

[3] "Adams methods", _NDSolve Method Plug-in Framework_,
http://reference.wolfram.com/mathematica/tutorial/NDSolvePlugIns.html

[4] _Monitoring and Selecting Algorithms_,
http://reference.wolfram.com/mathematica/tutorial/MonitoringAndSelectingAlgorithms.html