My Math Forum  

Go Back   My Math Forum > College Math Forum > Real Analysis

Real Analysis Real Analysis Math Forum

LinkBack Thread Tools Display Modes
June 17th, 2013, 06:24 AM   #1
Joined: Apr 2013

Posts: 20
Thanks: 0

Solving Recurrence equation

Hey, so I have:

I also have the initial conditions, a0 = 5 and a1 = 4.

I have to 'solve' it but I having issues.

Answer for general solution is:

And it then applies initial conditions to get solution:

My attempt so far has been unsuccessful. I know we use the homogenous equation but I cannot figure out how. Any help? Thanks!
One is offline  
June 17th, 2013, 08:28 AM   #2
Senior Member
MarkFL's Avatar
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,211
Thanks: 521

Math Focus: Calculus/ODEs
Re: Solving Recurrence equation

We first solve the associated homogenous equation:

which has the auxiliary equation:

Hence, a general solution to the homogeneous equation is:

Since the inhomogeneous term is , we seek a particular solution of the form:

where the constants and are to be determined. Substituting this expression for into the recursion, we find:

Equating coefficients, we find:

Thus, we have found:

and so:

Now, we may determine the parameters from the given initial values:

Solving this linear 2X2 system, we find:

and thus we finally have:

MarkFL is offline  
June 17th, 2013, 01:20 PM   #3
Math Team
Joined: Sep 2007

Posts: 2,409
Thanks: 6

Re: Solving Recurrence equation

Nicely done!
HallsofIvy is offline  

  My Math Forum > College Math Forum > Real Analysis

equation, recurrence, solving

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Need help finishing up with solving a recurrence restin84 Computer Science 1 October 10th, 2012 05:48 AM
Need help solving(another) recurrence restin84 Computer Science 1 October 5th, 2012 12:04 AM
Solving a recurrence restin84 Computer Science 4 September 19th, 2012 08:01 AM
solving recurrence hayood Computer Science 1 January 31st, 2011 12:52 PM
Solving recurrence relations with two variables mrbobbles Applied Math 1 May 9th, 2009 11:28 AM

Copyright © 2019 My Math Forum. All rights reserved.