Overview of the Demonstration Programs

Overview of the Demonstration Programs

G.D. Byrne
Departments of Applied Mathematics and
Chemical & Environmental Engineering
Illinois Institute of Technology
Chicago, IL 60616
S. Thompson
Department of Mathematics and Statistics
Radford University
Radford, VA 24142,


The demonstration programs illustrate the use of the Fortran 90 ordinary differential equation (ODE) VODE_F90 which is an extension of the well-known f77 VODE solver. VODE_F90 is applicable to initial value problems of the form

y'(t) = f(t,y(t)),        y(t0) = y0 .

Several extensions were incorporated in VODE_F90. In particular, it contains an option for root finding ("event location"); and it contains an option to accommodate sparse Jacobians. It has also an option to impose bounds on the solution y(t) . The demonstration programs illustrate the use of these options as well as others.

Most of the demonstration programs have an accompanying MATLAB script for plotting the solution generated by the program. To run the demonstration programs you will need to first obtain the solver file vode_double_m.f90 (or vode_single_m.f90) from the solver source code directory. If you encounter any difficulties with the demonstration programs or have questions regarding them, please contact the authors. Please note that the demo programs are still being refined; so they may change at any time.

The programs reside in directories each containing subdirectories for different problems. Following is a brief summary of what the various demonstration programs do and what each is intended to illustrate. If you click on the link for any demo program, you can download it and other related files.

Miscellaneous Demos

MOL Demos

Pitagora Demos

The programs in this directory solve problems from the well-known Pitagora test suite . The authors kindly permitted us to include their pdf descriptions of the problems solved by these programs. Refer to these descriptions for more details about the problems.

Toronto Demos

The programs in this directory solve problems from the well-known Toronto (DETEST) test suites.


The programs in this directory consist of demo programs for the ODEPACK family of integrators. These programs are included primarily for people familiar with their use in conjunction with the ODEPACK solvers and who would like to compare the results with those for the original solvers.

Single Precision Demo Programs

Several of the programs described above have single precision counterparts. Not all of the double precision demos were converted to single precision because we typically use double precision on computers with short single precision word lengths. Following is a list of the available single precision demos.