Introduction

All methods seen up to now are single step methods, in the sense that the approximation only depends on the previous result and not on other calculated results.

Multistep methods take the form

,

for .

These methods use previously calculated values to make the next estimate. They require initial values

,

where the must be calculated using a different method for .

>

When , the formula only uses values already obtained and is called `explicit' . can easily be calculated using the obtained values.

>

When , the values and appear on the right-hand-side as well, so that the formula becomes an iterative formula. In this case, the method is called `implicit'.