Introduction: The methods discussed so far have required knowledge of the differential equations and initial values only. Consequently, given an approximation to the value of at , say, , they have provided a technique for computing . They could therefore be called one-step methods because they only required the value at one mesh point to compute the value at the next. Once the values at a number of points, say for , have been computed, they can be used to obtain the solution at . Thus the methods which make use of the information about the dependent variable at , to compute the value of the dependent variable at are called multistep methods.

Consequently, a K-step multistep method is a method which uses the information about the dependent variable at K different mesh points to compute the value of the dependent variable at .