Re: Integration of stiff multidimensional ODE


In article <1177882304.166890.143400@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
hohenegger@xxxxxxxxx writes:
Hi,
I try to ingegrate a multidimensional system of ODE's (steming from a
discretized, nonlinear Boltzmann equation).
The 4th order Runge-Kutta and the Burlish-Stoer method turned out to
be stiff (stepsize is very low).
If possible I want to avoid computing the Jacobian. Therefore I am
searching for an explicit method.
The solutions can be expected to be smooth functions, so I thought
about using a predictor-corrector method (Adams-Bashforth).
Does anybody know a (freely available) implementation of such
algorithms in C?
in
http://www.netlib.org :
ode/cvode.tar.gz
for: large non-stiff or stiff ordinary differential equation initial-value problem solver
alg: combines earlier vode.f and vodpk.f
lang: C
by: Scott D. Cohen and Alan C. Hindmarsh
size: 273 kB
Score: 100%

Can I expect these methods to perform better?
no
the stability region of predictor / corrector codes are quite modest and
smaller than those off rk4




I would also be thankful for hints to other suitable methods.
Thanks,
Andreas


try
1. ode/rkc.f
for: explicit solver for parabolic PDEs
by: Sommeijer, Shampine, Verwer
ref: J. Comp. Appl. Math., submitted 1997
prec: double
lang: Fortran77
alg: second-order explicit Runge-Kutta-Chebyshev formulae
gams: I1a1a
Score: 100%

2. ode/rkc-exa.f
for: example A for ode/rkc.f
Score: 100%

3. ode/rkc-exb.f
for: example B for ode/rkc.f
Score: 100%

this is a multistage explicit Runge Kutta code with a largely extended
stability region (not only useful for the case indicated above)
hth
peter
.