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Math Help - ODE Solved Using Euler Method

  1. #1
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    ODE Solved Using Euler Method

    I get the feeling I'm making a mistake somewhere here since the error is extremely high

    Problem:
    Compute by hand using the Euler Method given:

    y' = -100y+1
    y(0)=1

    Attempt:

    Euler Method: yi+1= yi + h*f(ti,yi) where h is the arbitrary step size which in this case will be 0.1
    yi = 0
    h = 0.1
    f(ti,yi) = f(0,1) = -100(1) + 1 = -99
    yi+1= 1 + (-99)(0.1) = -8.9

    To calculate percent error, find the exact solution.
    Solving the ODE yields:
    y = 1/100 + 99/(100*e100t)

    Plugging in 0.1 for t yields approximately 0.01005 for the exact solution as opposed to -8.9 in the approximated solution
    Last edited by spruancejr; April 2nd 2012 at 06:56 AM.
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: ODE Solved Using Euler Method

    Quote Originally Posted by spruancejr View Post
    Euler Method: yi+1= yi + h*f(ti,yi) where h is the arbitrary step size which in this case will be 0.1
    yi = 0
    h = 0.1
    f(ti,yi) = f(0,1) = -100(1) + 1 = -99
    yi+1= 1 + (-99)(0.1) = -8.9
    In the 4th and 5th lines you've taken y_i as 1 instead of 0.
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  3. #3
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    Re: ODE Solved Using Euler Method

    Thanks!
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  4. #4
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    Re: ODE Solved Using Euler Method

    I incorrectly entered the initial condition.
    Last edited by spruancejr; April 2nd 2012 at 07:32 AM.
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