Solve does not give solutions to all variables

Question

I have a beam with $n$ points and I have to find a numerical solution of the axial force using Finite difference method

Here is my code

Ej = 210000; (* MPa *)
A = 200; (* mm^2 *)
EA = Ej*A;
n0 = 2; (* N/mm *)
L = 2000; (* mm*)
F0 = 1000; (* N *)
k = 1000; (* N/mm *)        
n = 3;(*number of points*)
    h = 2 L/n;(*distance between the points*)

    steps = Table[u[i], {i, 0, n + 1}];

    equations = Table[
       steps[[i + 1]] - 2 steps[[i]] + 
         steps[[i - 1]] == -h^2 n0/EA, {i, 2, n + 1}];

    BoundCondition = {steps[[2]] == 0, 
      steps[[n + 2]] - steps[[n]] == -F0 2 h/EA};

    Join[equations, BoundCondition];

    solution = Solve[equations, steps]

My idea was to use this code to get some numerical values for $u[i]$ for $i=1,...,n$ yet Solve leaves me an error: Solve::svars: Equations may not give solutions for all "solve" variables.

I am approximately 95% sure that the mathematical and physical background is ok so I have a strong feeling that I am doing something wrong in this code. Any idea what might that be?

It's like Mathematica doesn't understand my boundary condition $u[1]=0$.