A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
anyone able to help me with difference equations?
anonymous
 3 years ago
anyone able to help me with difference equations?

This Question is Closed

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0What specifically? I know a bit...

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0@vf321 sorry was watching the rugby :D. how do you take two recurrance equations ( i think thats correct term) and create a difference equation that relates the two. More specifically...

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[d _{n}=2p_{n}+3 \] and \[s _{n+1}=p^{2}_{n}+1\] need a difference equation that relates \[p_{n+1}\] to \[p_{n}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Well hang onwhat is the relation between \(d_n\) and \(s_n\)?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0you may need the information that P_{n} represents price per unit in period n. s_{n}, d_{n} represents supply and demand respectively. the question says asumming market price is price at which supply equals demand... i think that is answering what you have just asked.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0OK then. Well, then what's the problem?\[s_{n+1} = d_{n+1} = 2 p_{n+1}+3\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0but d_{n} is given, not d_{n+1}

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Yes, but that's the point of difference equations  they're true for all integral \(n > 0\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Or, depending on your definitions, \(n = 0\) may be valid too.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so, d_{n+1} is simply 2p_{n+1}+3

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yeah. Given that, can you replace \(s_{n+1}\) in the other equation?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0BTW, for inline latex surround your formula in \.(formula\.) ( without the periods)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so the difference equation would be 2p_{n+1}+3=p^{2}_{n}+1, and rearranged?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Correct. Do you have Mathematica?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Mathematica, no. is it software?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Yes, it would let you solve the difference equation if you needed to.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh... I use maple. pretty sure that will help solve it. also thanks for the tip on the inline latex. been wandering how to do that for ages.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0do you know about steady states? because thats what i am asked to find.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Hmm. If I had to guess (so, no, I haven't really done them before), then I would say that steady states are situations where the price has asymptotic behavior, so as \(n\) goes up, \(p_n\) continually gets closer to a certain value.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0hmm ok. Well I think the steady states are a diferrent way of saying stationary points. as we were taught them with an example using dx/dt=f(x*) and the steady states were solutions of f(x*)=0.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0not sure if that will change the way you think about it.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh ok. so do you have an idea on how you would approach finding steady states of a difference equation?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Well, (and again I dont know for sure), being in a steady state for something discrete like a difference equation probably means solving \(p_{n+1}p_{n} = 0\), because the difference between the two steps is 0 means it's in a steady state.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0And you already have a formula for \(p_{n+1}\), so I would just plug it in and solve.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh ok. that makes sense. well anyway i guess that is everything. thanks for the help.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.