Abstract
In this paper, our aim is to study the numerical solution of initial value problems (IVPs) for ODE´s is one of the fundamental problems in scientific computation. There are many well-established algorithms for approximate solution of IVPs. However, traditional integration methods usually provide only approximate values for the solution. Precise error bounds are rarely available the error estimates, which are sometimes delivered, are not guaranteed to be accurate and are sometimes unreliable. The main goal of the paper is to present all the existent approaches together emphasizing that since, all researches face the same problem but in different contexts, they are finding the same kinds of problems in spite of there different for mails m5 and methodologies.
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