We shall now describe methods for solving a scalar IVP

Most of the methods that follow can be easily extended to vector systems. Since it is assumed that the given IVP is not amenable to analytical solution, we approximate its solution at a set of discrete points, called the mesh (or grid) points. We subdivide the internal into a finite number of equally spaced subintervals as

where

and is called the mesh (or step) size. Since the solution at is known (initial condition), we need to approximate the solution at the grid points for

A method which involves the knowledge of the solution only at the previous point in order to find the solution at the current point , is called a single step method.