1. The problem statement, all variables and given/known data Imagine a chain with ##n## links across a river. Now imagine, the chain is in a straight horizontal line at time ##t=0##. The problem wants me to calculate the movement of the chain links (center of mass) due to the gravity field. There are other forces in the system but this should give you an idea what I am doing - I am having problems with finding a numerical solution not the physical understanding. My variables are in fact angles between the chain link and horizontal line. Knowing the angles, determines the system completely. Applying equations of motion to each rod should give me a result. 2. Relevant equations I am using the Lagrange's approach with Lagrange's equations of the second kind. 3. The attempt at a solution Sadly the system is a bit more complicated than I described. There are torsional springs between the links and also an external force than leads to energy dissipation. This leads to.. well... to some very long and rather complicated partial differential equations. Not something one would like to solve on a paper, so I decided to write something in Mathematica. On my dropbox link you will find my code that works really nicely in case of ##n=4##. LINK: https://www.dropbox.com/s/ev2ig6g5bfybbjd/seminar_1_arbitrary.nb?dl=0 The problem is that I don't get a solution for ##n## greater than 4. The differential equations and boundary conditions are correct (I checked 235235 times), but as soon as I increase n to 6 or 8 or 10, NDSolve doesn't do what it should anymore. So my question here is: If there are any Mathematica masters here? - What can I do? And to others: What are the most commonly used methods for solving a rather big system of PDEs? Is Mathematica even the right tool to do this? According to google, matlab is a good tool to, but sadly, I have never worked there and I assume would be a nightmare to start with an example like that.