My Math Forum  

Go Back   My Math Forum > College Math Forum > Applied Math

Applied Math Applied Math Forum


Reply
 
LinkBack Thread Tools Display Modes
January 28th, 2012, 11:24 PM   #1
Newbie
 
Joined: Jan 2012

Posts: 5
Thanks: 0

changing difference equation

I have to change this systems of difference equation to a single higher order equation.





The answer is



What I did so far was set it equal to zero and got this:



I am not sure what to do after. I think I am supposed to find the characteristic equation but my equation doesn't look like a polynomial.
Can someone help me figure this out please?
Thank you for your time!
uterfor86 is offline  
 
January 28th, 2012, 11:27 PM   #2
Newbie
 
Joined: Jan 2012

Posts: 5
Thanks: 0

Re: changing difference equation

Whoops. I made a mistake on the second equation. It is

uterfor86 is offline  
January 29th, 2012, 12:01 AM   #3
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,205
Thanks: 512

Math Focus: Calculus/ODEs
Re: changing difference equation

We are given:

(1)

(2)

Method 1:

Taking (2) and replacing n with n + 1 gives:



Using (1), substitute for :



Solving (2) for and substituting, we then get:









Now we have a linear homogeneous recurrence, whose associated characteristic equation is:





Thus, we find the closed-form for is:

where A and B are arbitrary constants.

Method 2:

Taking (1) and replacing n with n + 1 gives:



Using (2), substitute for :





Solving (1) for and substituting, we then get:







Now we have a linear homogeneous recurrence, whose associated characteristic equation is:





Thus, we find the closed-form for is:

where A and B are arbitrary constants.
MarkFL is offline  
Reply

  My Math Forum > College Math Forum > Applied Math

Tags
changing, difference, equation



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
period difference over changing frequency binarygoodmathpoor Calculus 1 February 12th, 2014 07:33 AM
difference equation capea Complex Analysis 3 September 11th, 2013 01:09 AM
Difference Equation bilano99 Calculus 4 March 22nd, 2012 04:58 PM
difference equation uterfor86 Applied Math 1 January 15th, 2012 10:38 PM
Help with difference equation BlackKnight Applied Math 0 March 15th, 2009 11:25 AM





Copyright © 2018 My Math Forum. All rights reserved.