# Crank Nicolson Scheme For Heat Equation

• Aug 23rd 2006, 04:06 AM
Red_Fox
Crank Nicolson Scheme For Heat Equation
Hi everybody!
I need to use the Crank-Nicolson method to solve the following Heat Equation (PDE), but unfortunately I haven't found yet any efficient material about it, neither books nor the web. I know what is its form, and other details about it, but in fact - how to do that thing - I have no idea...

My Equation:
(1) U(x,t)'t = a*U(x,t)''x
Initial & Boundary Conditions:
(2) U(x,0) = T0
(3) -k*U'(0,t)x = q
(4) -k*U'(d,t)x = h*(U(d,t)-T1)

when a, TO, T1, k, q, d, and h are all constants!
Pay attention that the conditions (3) and (4) are on the derivative of U.

Thanks (:
RedFox.
• Aug 23rd 2006, 04:38 AM
CaptainBlack
Quote:

Originally Posted by Red_Fox
Hi everybody!
I need to use the Crank-Nicolson method to solve the following Heat Equation (PDE), but unfortunately I haven't found yet any efficient material about it, neither books nor the web. I know what is its form, and other details about it, but in fact - how to do that thing - I have no idea...

My Equation:
(1) U(x,t)'t = a*U(x,t)''x

I assume this means:

$
\frac{\partial U}{\partial t}=a\ \frac{\partial^2 U}{\partial x^2}
$
?

(This is a question)

Quote:

Initial & Boundary Conditions:
(2) U(x,0) = T0
(3) -k*U'(0,t)x = q
(4) -k*U'(d,t)x = h*(U(d,t)-T1)

when a, TO, T1, k, q, d, and h are all constants!
Pay attention that the conditions (3) and (4) are on the derivative of U.

Thanks (:
RedFox.
I would have thought that this pdf file would provide all you need to know.

RonL
• Aug 23rd 2006, 05:26 AM
Red_Fox
Well..
first, thank you very much!
by the way, of course I mean to that...

I am skimming this document, and it seems to be pretty good (:
I just wanted to ask, if still someone has any other material about that subject, mainly about full solutions of equations with Crank-Nicolson scheme, which can really help me.

Thank you all,
and especially to CaptainBlack, for the quick reply (:
RedFox.