RADAU5 Fortran 77 ODE Solver

RADAU5 is an ODE solver written by Ernst Hairer and Gerhard Wanner.

The VFGEN RADAU5 Command

A Fortran 77 file that can be used with RADAU5 is created by the command

$ vfgen radau5 vector_field_file.vf

This command creates the Fortran file [name]_rhs.f, where [name] is the name of the vector field given in the vector field file. The file contains the following subroutines:

Options

demo If the option demo=yes is given, the file [name]_dr5.f is also created. This program provides a sample driver for the RADAU5 subroutine. The initial conditions and parameter values are the default values defined in the vector field file.
Default: demo=no

Notes

Example

Here is a sample vector field file: vanderpol.vf.
The files created by

$ vfgen radau5:demo=yes vanderpol.vf
are

The files radau5.f and dc_lapack.f can be downloaded from the RADAU5 web site. I will use the gfortran Fortran compiler. In a Linux (or similar) system, in which the LAPACK library is installed in a standard location, the following commands will compile and run vanderpol_dr5. (In Mac OSX 10.5, I replace -llapack with -framework vecLib.)

$ gfortran -c radau5.f
$ gfortran -c dc_lapack.f
$ gfortran -c vanderpol_rhs.f
$ gfortran -c vanderpol_dr5.f
$ gfortran vanderpol_dr5.o vanderpol_rhs.o radau5.o dc_lapack.o -llapack -o vanderpol_dr5
$ ./vanderpol_dr5 > vdp.dat
The last command runs the program and sends the output to vdp.dat. Here is a plot of the data:
Graphs of x(t) and y(t)