linear difference eqn-scary exams

Dear Mathematicians,

I have a question for you.thanks.

Lets say that you had to use a linear difference equation to solve some population problem.

How do you determine how many orders it is ?ie.first order,second order,3rd order etc.

eg.so how would I determine (if I am finding for n+1 or not)the long term chance of survival after contracting a deadly virus.

Re: linear difference eqn-scary exams

A linear difference equation can be written in terms of "differences", ( , , etc.) or in terms of different subscripts: , , etc.. The "order" of a difference equation is, in the first case, the largest power of and, in the second, the largest "n".

For example is a third order equation because of the .

Since , , and that same equation can be written as . That, again, has order 3 because of the "n+3".

Quote:

eg.so how would I determine (if I am finding for n+1 or not)the long term chance of survival after contracting a deadly virus.

I don't understand the "e.g.". Knowing the order does not greatly help in solving the equation. There are a large variety of ways of solving such equations.