Physics 381C: Solution of ODEs
Please report all errors/typos. etc to
matt@infeld.ph.utexas.edu
- General Reference
- Lecture 3 (Feb 18)
- Sample output illustrating
use of some utility commands: dvmesh, nf and
paste, which I will use from time to time, and which
you may find useful.
- lsoda.f:
ODEPACK routine for solving general systems of ODEs
- tlsoda.f Sample
driver routine which uses lsoda to integrate
u''(x) = -u(x). Sample
usage on SGIs.
Plot of computed
and exact solution on x = [0 .. 15] with all error tolerances
set to 1.0d-6. Plot of error in
computed solution. Plot of
error in
computed solution with all error tolerances set to 1.0d-8.
Makefile.
- integral.f:
Driver routine illustrating use of LSODA (ODE integrator)
to compute definite integral.
fcn.f:
User function which defines integrand.
Sample
usage on SGIs.
Makefile
- Lecture 4 (Feb 20)
- sode.f:
Another driver routine for LSODA which forms the basis
for the application programs discussed in class.
This version also solves u''(x) = -u(x).
fcn.f:
User function defining right hand-sides of ODEs.
Makefile
- orbit.f:
Driver routine illustrating use of LSODA to solve restricted
2-body gravitational problem (one body non-gravitating).
fcn.f:
User function which implements equations of motion.
Makefile
- The orbiting dumbbell problem:
- Equations of motion (PS)
- dumb.f:
Driver routine for solution of orbiting-dumbbell problem.
fcn.f:
User function which implements equations of motion.
Makefile
- Plots of omega (angular frequency of dumbbell about its
center of mass) versus time for a
circular orbit
and for an
elliptical orbit.
Note the "chaotic" nature of omega in the latter case.
Detail
of omega for the elliptical orbit.
- Plots illustrating energy conversation for elliptical
orbit (chaotic case).
Energy quantities
computed with LSODA tolerance 1.0e-6.
Top to bottom: Translational
kinetic energy, rotational kinetic energy, total energy,
gravitational potential energy. In this case, "non-conversation"
of total mechanical energy is a good sign that we need to
make the error tolerance more stringent.
Energy quantities
computed with LSODA tolerance = 1.0e-12. Note that
energy conservation is improved in this case.
Plot of
rotational kinetic energy.
- Lectures 5 and 6 (Feb 25, 27)
- deut.f: Driver routine
for solution of toy deuteron model using shooting.
fcn.f:
User function which implements equations of motion.
fcn.inc:
Parameters and common block for communication with user function.
Makefile
PS plot and
detail of several
trial solutions generated via binary search on eigenvalue, E.
Plot of computed eigenfunctions for
various values of parameter, x_0. Note that eigenfunctions are
not normalized.
Supermongo (SM) sources for plots:
[1],
[2],
[3]
- bstars.f: Driver routine
for solution of relativistic boson star model using shooting.
fcn.f:
User function which implements equations of motion.
fcn.inc:
Parameters and common block for communication with user function.
Makefile
Plot of computed scalar field
profiles for Lambda = 0 and Lambda = 100 with sigma_c = 0.1. Compare
with Figure 3 of Colpi et al.
SM source for plot.