Solve the recurrence relation :

an= 2an−1−2an−2

subject to the initial conditions

a0 = 1, a1 = 3.

Printable View

- Oct 10th 2010, 01:30 PMaamiriRecurrence Relation Problem...

Solve the recurrence relation :

an= 2*an−*1*−*2*an−*2

subject to the initial conditions

*a*0 = 1*, a*1 = 3*.*

- Oct 10th 2010, 01:44 PMpickslides
First solve the characteristic equation $\displaystyle s^2-2s+2= 0$

What do you get? - Oct 10th 2010, 01:55 PMaamiri
- Oct 10th 2010, 02:02 PMpickslides
That sounds right.

The next step is to put these solutions into polar form. Once you have done this, the general solution to the recurrance relation will be of the form

$\displaystyle \displaystyle a_n = r^n(\alpha \cos n\theta +\beta \sin n\theta)$

using $\displaystyle a_0=1,a_1=3$ to solve for $\displaystyle \alpha$ and $\displaystyle \beta$ - Oct 10th 2010, 02:12 PMaamiri
- Oct 10th 2010, 02:41 PMpickslides