Module 4: Systems of Equations and Equations of Order Greater Than One
Lecture 13: Direct Methods For Higher Order Equations
Rather than expand a higher order equation into a larger system, we have direct methods to solve them. Here we will outline the extension of some of the one-step methods to higher order equations such as (4.1).
Taylor's Series Methods
The Taylor's series method can be extended in the obvious way as follows: We are given . Using (4.1) we can calculate and by differentiation of (4.1) a number of times we can also
. Using (4.1) we can calculate 
and by differentiation of (4.1) a number of times we can also 
. We can then write 
can be approximated at 
.
