To solve this problem one must solve a system of differential equations which contains trigonometric functions (sin) . Not every algorithm will give a stable solution when used for this. There are four different algorithms in the program. Three of them are user written (Euler, Mid-point and Verlet ), and the fourth is the IMSL routine IVPAG. IMSL is mathematics library which enables one to use its routines in order to solve different mathematics problem. The Euler algorithm and IVPAG give stable solutions, and the Mid-Point and Verlet give a non convergent solution. This can be seen by monitoring the total energy of the system (with driving force and friction zero) through a few runs of the program. Integration time can be changed only for the first three algorithms. If you change it you can check if the solution is more or less stable (again by monitoring the energy). There is also a possibility to do the integration backward (by clicking the Inv. time). In this case you should see a backward motion on the screen, the oscillators should return to the start position, and the energy should be the same as in the beginning (when friction force is zero). If you continue running the program for some time, you should notice that the oscillators are entering some stable mode of motion.

This project uses FORTRAN,PGPLOT and IMSL; the programs can be obtained by http from the Computational Physics http server. They are compiled on AIX machines such as turbo and minerva1 with the command

" xlf -o !:1.ex -L/usr/local/lib -lpgplot -lX11 $FFLAGS !:1.f $LINK_FNL " .

On tx replace xlf with f77 for the same results. You need to write

source /usr/local/imsl/setup.csh

before compiling on Technion machines,
more information on compilation and on this project
by *email.*

Last updated on : Sun May 31