The linear multi-step method in this work is established to be a numeric fixed point iterative method forsolving 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 consistencyconditions were discussed while section two is devoted to theoretical presentation of the usual Hamming’smethod as a fixed point iterative m...

research work presents an important Banach Space in functional analysis which is known and called Hilbert space. We verified the crucial operations in this space and their applications in physics particularly in quantum mechanics. The operations are restricted to the unbounded linear operators densely defined in Hilbert space which is the case of prime interest in physics, precisely in quantum machines. Precisely, we discuss the role of unbounded linear operators in quantum mechanics partic...