On Sep 30, 8:39 am, Luke <hazelnu...@gmail.com> wrote:
> The methods you suggest essentially takes care of the mass matrix
> problem by solving a linear system numerically during numerical
> integration. I am familiar with tools out there that do this, but
> this isn't what I'm looking to do. I haven't seen one that is written
> directly usable in Python -- do you know of one? The netlib packages
> have this capability, but I'm no Fortran programmer.
>
> What I am interested in doing is solving the linear system
> symbolically so that first order equations can be generated
> symbolically and the most generic of ODE solvers will work. This also
> eliminates the iteration that is being done by the ODE solver during
> time integration.
>
By eliminating iteration here I mean eliminating the iterations of the
root finding / linear system solving algorithm, not adaptive time
stepping type iteration.
~Luke
> Thanks,
> ~Luke
>
> On Sep 29, 8:07 pm, Tim Lahey <tim.la...@gmail.com> wrote:
>
> > On Sep 29, 2009, at 7:15 PM, Alan Bromborsky wrote:
>
> > > Are there differential equation solvers where you don't have to invert
> > > the matrix?
>
> > A Newmark-Beta scheme will directly solve a second-order system of ODEs.
> > The standard form uses iteration to solve the system so no inversion is
> > necessary. For linear second-order problems you can rewrite things to
> > use matrix algebra.
>
> > For more information, I recommend Bathe and Wilson,
>
> > Klaus-Jürgen Bathe and Edward L. Wilson. Numerical Methods in Finite
> > Element Analysis. Prentice Hall, Englewood Cliffs, New Jersey,
> > 1976.
>
> > There are other second order solvers out there too.
>
> > Cheers,
>
> > Tim.
>
> > ---
> > Tim Lahey
> > PhD Candidate, Systems Design Engineering
> > University of Waterloohttp://www.linkedin.com/in/timlahey
>
>
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