How to compute a finite difference with variables that are arrays

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DIP
DIP 2017-4-7
编辑： DIP 2017-4-7
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

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