Re: TWO questions to experts ...

[Aiviet Nguyen <aiviet@cat.syr.edu>]

Hi Anh Quoc-Lan,
   The CERN Library package can be listed from any Physics Department 
that affiliates with CERN. You may want to try with some Physics 
Institution nearby.
   There are few different programs for ODE and PDE in those packages 
for your taste. I think the algorithm just for solving the equation is 
not interesting. The strength of CERN packages is the error control and 
the stability of the program. These codes have been written and tested 
again and again on High-Energy Physics projects ( The largest number 
punching benchmarks in the world). We can consider them as perfect at 
least at the level of VNSA.
  In the C or Fortran Recipes by the group of Cornell you can find
very simplified version of the used algorithm without strong error 
controls. Those recipes are good for daily use and for non-stiff 
equations.
   I like the Runge-Kutta shooting for boundary condition problems
and finite element methods.
   I don't think that in Algorithms we have some big discovery. This 
area has been well explored by generations. My friend an expert in
Computing Hydrodynamics said that nowaday all algorithms are the same.
You can look at NASA archives for a lot of Algorithms in PDE and ODE.
I am sorry that I also share the same viewpoint with my friend so has been
trusting only in well tested algorithms.
Cheers
Aiviet    

    

On Thu, 27 Mar 1997, Quoc-Lan Nguyen wrote:

> > Sure, there are quite a lot in Fortran and in C. You can also write one 
> > by yourself if no additional requirements are needed.
> > The standard library package of CERN or CORNELL has very good error control
> > and very stable.
> >   The program does not know that the equation has solution or not. So if 
> > you specify a smalll error, the algorithm will not be convergent and will 
> > loop forever. If you specify a large enough error, it will output some 
> > solution depending on the starting point.
> >   Cheers
> >   Aiviet
> > PS: Are you interested in the Algorithm they use in those packages?
> 
> Xin phep' bac' Aiviet de tui chen vo. Tui quan ta^m de^n' cac' Algorithm xu dung
> trong cac' pha^n` me^m` do', cang` ty? my? cang` to^t'. Cha*ng? hay bac' Aiviet
> co' the^? cho bie^t' dia chi? de^? tim` doc?
> 
> Cam' o*n truo*c',
> 
> QLa^n 
>