I have to create a program that compares two or three different methods (FEM FVM FDM) for solving an easy pde. Is there a program language in which I could do this easily? (i need to operate with vectors/matrix and perform inversions on matrix)
For this kind of data processing I would really recommend R (note that I'm a heavy R user, so I might be biased. But let me break it down a bit. I would definitely go for a high level language like Python + numpy, Matlab or R, and not Fortran or C++. These languages are powerful I know from experience, but also more complex. If it is not strictly needed I would stick to a simpler language, this will enable you to spend more time analyzing data and less programming.
In choosing a high level language, I'd go for R. It is free and open source, has powerful data processing routines built-in, awesome visualisation tools, and a very large user community that provides even the most exotic analysis methods. Although you'd probably also work happily with some other high level language.
My suggestion would be to use Python. The SciPy package allows for solving PDE really simply. I used it for the projects involved in my honours thesis and found it really easy to learn and simple. Have a look at http://scipy-lectures.github.com/intro/scipy.html#numerical-integration-scipy-integrate .