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Thread: solving one dimension steady state heat equation with finite differences

  1. #1
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    solving one dimension steady state heat equation with finite differences

    I have a project where I need to solve

    T''(x) = bT^4 ; 0<=x<=1
    T(0) = 1
    T'(1) = 0

    using finite differences to generate a system of equations in Matlab and solve the system to find the solution

    So far I have:
    (using centred 2nd degree finite difference)
    T''(x) = (T(x+h) - 2T(x) + T(x-h)) / h^2 = bT(x)^4
    and
    (using 2 order backward difference)
    T'(x) = (3T(x) - 4T(x-h) + T(x-2h)) / 2h

    I just don't know how to write the code that will make the system of n non-linear equations to solve. I have a function that will solve them if I can get there...

    any help or nudge in the right direction is appreciated

  2. #2
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    Quote Originally Posted by Arkady View Post
    I have a project where I need to solve

    T''(x) = bT^4 ; 0<=x<=1
    T(0) = 1
    T'(1) = 0

    using finite differences to generate a system of equations in Matlab and solve the system to find the solution

    So far I have:
    (using centred 2nd degree finite difference)
    T''(x) = (T(x+h) - 2T(x) + T(x-h)) / h^2 = bT(x)^4
    and
    (using 2 order backward difference)
    T'(x) = (3T(x) - 4T(x-h) + T(x-2h)) / 2h

    I just don't know how to write the code that will make the system of n non-linear equations to solve. I have a function that will solve them if I can get there...

    any help or nudge in the right direction is appreciated
    This is a boundary-value problem (as opposed to initial value problem).

    There are several methods of solving these - which method did you want to use?
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  3. #3
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    I want to use a numerical method. I need to discretize the problem by posing n points equally spaced by h. Apply the two finite difference equations in the previous post to come up with a system of n+1 equations.
    Once I have that system of equations, I will be able to solve the problem...
    I am not sure that this is a boundary value problem since I am given T(0)=1 and dT(1)/dx = 0
    I thought boundary problems were when we know T(0) and T(1) ?
    Last edited by Arkady; 08-01-2012 at 04:03 PM.

  4. #4
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    I found this
    http://www.mathworks.com/matlabcentr...ference-method
    that seems to get me a bit closer. However I cannot use the program as is because I only know the value of the derivative at x = 1 ...

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