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Math Help - Numerical Integration of ODE

  1. #1
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    Numerical Integration of ODE

    Find using Euler approximation to the solution of Initial Value Problem:

    y' = x - y - 2
    y(0) = 2
    [0,1], with step h = 0.1

    My solution
    I find:
    y_1 = 1.6; x_1 = 0.1
    y_2 = 1.25; x_2 = 0.2

    Analytical Solution:
    y(x) = \frac{x^2}{2} - 2x
    y(x_2) = -0.38
    Global error: -0.38 - 1.25 = -1.63
    It's correct ???
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Apprentice123 View Post
    Find using Euler approximation to the solution of Initial Value Problem:

    y' = x - y - 2
    y(0) = 2
    [0,1], with step h = 0.1

    My solution
    I find:
    y_1 = 1.6; x_1 = 0.1
    y_2 = 1.25; x_2 = 0.2
    You are asked to solve this over the interval [0,1] so you will have 11 points corresponding to x=0,0.1,..1.0

    Analytical Solution:
    y(x) = \frac{x^2}{2} - 2x
    y(x_2) = -0.38
    Global error: -0.38 - 1.25 = -1.63
    It's correct ???
    Your analytic solution does not satisfy the initial conditions!

    CB
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    You are asked to solve this over the interval [0,1] so you will have 11 points corresponding to x=0,0.1,..1.0



    Your analytic solution does not satisfy the initial conditions!

    CB
    The analytical solution would be:
    y(x) = \frac{x^2}{2} + x(y-2)
    ??
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  4. #4
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    Quote Originally Posted by Apprentice123 View Post
    The analytical solution would be:
    y(x) = \frac{x^2}{2} + x(y-2)
    ??
    You've actually gotten colder, compared to your original post. This is also a linear first order inhomogeneous ode and can be solved by various means, i personally opted for finding an integrating factor, for both this equation and for the other equation in the Runge-Kutta thread. I need to sleep now but you should be able to find all the details you need to find the solution at, Integrating Factor -- from Wolfram MathWorld .

    EDIT: Well don't i feel silly, should have pointed you here first, http://www.mathhelpforum.com/math-he...ial-38182.html .
    Last edited by RiseAgainstMe; November 12th 2010 at 12:49 PM.
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