### General principles

Before we look at specific integration schemes, it is useful to start by posing the problem of numerical simulation in a general way and then looking at how numerical integration approaches its solution. We then discuss the general characteristics of integration schemes and review some terminology associated with different types of schemes.

#### Statement of the problem

Numerical integration is a method of solution of a problem. So what is the problem we are trying to solve?

##### Motion of a particle as an initial value problem

To simplify the discussion, consider the problem of simulating the motion of a single particle under the action of forces. Suppose the particle starts out at a location given by its initial position vector **×**