hello ... i am new with cygwin ... and i want you to help me. ...
First of all, i want to determine the steady state stream function in a 2-D duct using a square mesh by using the finite-difference methodology and i want to simulate it....and i read a lot of information at http://dehesa.freeshell.org/ avout vogle that make graphs and FDLIB ...can you tell me what to

FDLIB is a shared library that you link your own code against. If you do not already write your own programs, this is going to be a daunting task.
1. develop your own simulation model - it seems there are tutorials on the site you gave --use those
2. install FDLIB - instructions come with it
3. compile your code against FBLIB, gcc myfile.c -o myfile -libfdlib
-- note: I made up "-libfdlib" the tutorial will give you how to link against FDLIB
4. run it against data, producing output files

vogle must be graphing software - that usually means you have write a script to tell it how the incoming data is defined and how to generate the graph. Some graph packages have their own "language" to program their use.

You are going to need help from someone who can look over your shoulder. Doing this by remote control via the these forums is not very efficient.