- #1
Benny
- 584
- 0
Hi I'm just wondering what difference/recurrence equations are about. From what I can recall from the bits and pieces I've readed, difference equations are somewhat similar or an analogue of differential equations. I've read through some things on first and second order difference equations but I don't really understand what they are about.
My book introduces difference equations as summations. They seem to be equations involving summations with different indices. I know what I've said is a little vague so here is an example question I have(not from the book I referred to).
Q. Find the general solution of the following difference equation.
[tex]y_{n + 1} - y_n = 2[/tex]
Answer: [tex]y_n = A\left( {\frac{1}{2}} \right)^n + 2[/tex]
Can someone explain to me what the equation actually means?. Any sort of explanation or references to useful websites would also be good. As I alluded to before I don't actually see the connection between difference equations and differential equations. Is it like when you have a real function f(x) and you the sequence f(n)? Any help would be appreciated.
My book introduces difference equations as summations. They seem to be equations involving summations with different indices. I know what I've said is a little vague so here is an example question I have(not from the book I referred to).
Q. Find the general solution of the following difference equation.
[tex]y_{n + 1} - y_n = 2[/tex]
Answer: [tex]y_n = A\left( {\frac{1}{2}} \right)^n + 2[/tex]
Can someone explain to me what the equation actually means?. Any sort of explanation or references to useful websites would also be good. As I alluded to before I don't actually see the connection between difference equations and differential equations. Is it like when you have a real function f(x) and you the sequence f(n)? Any help would be appreciated.