Math Is Fun Forum

nha

Member

Registered: 2010-09-05

Posts: 43

exact solution to heat equation

Hey everyone, I need a little help with this question.

Relevant equations:

The question:

Let

and

, given the initial condition

, what is the exact solution at points on the grid?

So I have worked out

and

, and then worked out

.

I am just unsure what the exact solution is, since I don't know k.

Can someone help me with the exact solution.

Thanks

Last edited by nha (2010-10-11 02:23:13)

nha

Member

Registered: 2010-09-05

Posts: 43

Re: exact solution to heat equation

Am I supposed to find

which gives the exact solution at points on the grid, and that

and

. I can't find what

is.

All I have is:

,   

where

.

I still need some help.

Thanks

Last edited by nha (2010-10-11 02:46:27)

boy15

Member

Registered: 2010-03-29

Posts: 16

Re: exact solution to heat equation

Am I supposed to find

which gives the exact solution at points on the grid, and that

and

. I can't find what

is.

I think you need to find T(j,n), but I don't know what the exact solution is. I guess you will have to wait for a moderator to answer, bobbym should be able to help you.

boy15

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: exact solution to heat equation

Hi boy15;

bobbym should be able to help you.

If you meant that sarcastically then I have to swallow it because I have been known to mess up.
If you really meant that, then boy do I wish that were true.
Truth is I am not even sure how solve the recurrence. I should know but I am drawing a blank with it.

Sorry nha, no help yet.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

nha

Member

Registered: 2010-09-05

Posts: 43

Re: exact solution to heat equation

Hi boy15;

bobbym should be able to help you.

If you meant that sarcastically then I have to swallow it because I have been known to mess up.
If you really meant that, then boy do I wish that were true.
Truth is I am not even sure how solve the recurrence. I should know but I am drawing a blank with it.

Sorry nha, no help yet.

I am sure he really meant it since you help almost everyone on here!

Well, how would I evaluate:

, 

where

.

I know I need to use:

for all n

and

but I can't seem to get much.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: exact solution to heat equation

Hi nha;

Have you looked at:

http://en.wikipedia.org/wiki/Heat_equation

About a third of the way down the page they talk about solving it using Fourier Series. This is the nearest thing I can see to your approach.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.