Question: Numerical Methods within the N body problem

I am looking for help with basic algorithms to approximate numerical solution to the N body problem. I have been trying to develop basic algorithms using Runge Kutta, Euler ect. Initially I specified to the 3 body case and the equations of motion. I am now trying to develop a more general algorithm. If anyone has knowledge in this are or can look through my annotated procedure to see where I have gone wrong I would appreciate it. I am very new to maple and would appreciate detailed exposition, "for dummy's", if you will. Thanks in advance
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