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Math Help - Crank Nicolson Scheme For Heat Equation

  1. #1
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    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.
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  2. #2
    Grand Panjandrum
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    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:

    <br />
\frac{\partial U}{\partial t}=a\ \frac{\partial^2 U}{\partial x^2}<br />
?

    (This is a question)

    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
    Last edited by CaptainBlack; August 23rd 2006 at 04:50 AM.
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  3. #3
    Newbie
    Joined
    Dec 2005
    Posts
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    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.
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