How to compute a finite difference with variables that are arrays

Hi, I have to compute the above. The methodology is

1. Solve initial condition X(1), X(2), X(3)
2. Solve for i using the previous and subsequent nodes
3. For the new i+1 values, re-solve for i using the new i+1 values across the  domain 
4. Compute the Xi until the value at i=n have converged between previous and new values.

X and Y are arrays. Can you help me with a tutorial or a pseudo code so that I can attempt to solve this ? Any help is greatly appreciated.

Thanks