The linear multi-step method in this work is established to be a numeric fixed point iterative method for solving the initial value problem. Such that when βk ̸= 0, the method is called implicit or otherwise, it is called an explicit method. In section one, preliminaries of the linear multi-step methods bordering on the truncation errors and consistency conditions were discussed while section two is devoted to theoretical presentation of the usual Hamming’s method as a fixed point iterati...