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Math Help - An equation that doesn't want to be numerically solved

  1. #1
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    An equation that doesn't want to be numerically solved

    Dear Sirs/Madams.

    I'm trying to solve numerically this equation:

    K1= (Jp/J0) * ( (J0-B) / (Jp-B) )
    K2= ( (1/Jp) - (1/J0) )

    t= (1/(A*B^2)) * ln ( K1 - B * K2) <- this is the equation

    Where t, J0, A and B are constants
    and Jp is unknowned.

    In my example:

    t=0.1
    A=1,88E+05
    B=6,974

    When I try to solve numérically (bisection method and secant method),
    log of a negative value doesn't exist and then there is an error.

    I have transformed the equation into another one, taking exponential function left and right
    and then the value of the exponential is a very big number
    and the method fails too (note that A is a big number).
    I have tried with Matlab.

    I'm sure the solution exists because
    I have had the A an B values using
    a mathemathical software (MathCad).

    Does anyone have a solution
    or an idea to solve this problem ?

    I will be very gratefull to you.
    Thanks in advance.

    Pepelu.
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  2. #2
    mfb
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    Re: An equation that doesn't want to be numerically solved

    What is J0?

    WolframAlpha finds a solution, but the implicit plot is not really useful.
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  3. #3
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    Re: An equation that doesn't want to be numerically solved

    Thank you 'mfb' for your answer!

    I forgot to mention that J0 is another constant.
    However, I think that the equation in WolframAlpha is not the same that I wrote.
    Inside the log there must be (K1-B K2).
    In addition, WolframAlpha does not tell how it is solved.
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  4. #4
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    Re: An equation that doesn't want to be numerically solved

    I'm sorry, I forget to mention that J0 is equal to 0.9 in my example
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  5. #5
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    Re: An equation that doesn't want to be numerically solved

    The equation will be:
    0.1 = 1/ (1.88*10^5 * 6.974^2) * ln ( ((x/0.9)* ((0.9-6.974) / (x-6.974))) - 6.974* ((1/x)-(1/0.9 )))

    The Wolfram solution is wrong: -1.627 e^-397105
    The correct answer (I know it) is arround J=0.9

    Any other idea ?
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  6. #6
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    Re: An equation that doesn't want to be numerically solved

    Quote Originally Posted by Pepelu View Post
    The equation will be:
    0.1 = 1/ (1.88*10^5 * 6.974^2) * ln ( ((x/0.9)* ((0.9-6.974) / (x-6.974))) - 6.974* ((1/x)-(1/0.9 )))

    The Wolfram solution is wrong: -1.627 e^-397105
    The correct answer (I know it) is arround J=0.9 <-- but then your equation is wrong

    Any other idea ?
    I've copied your equation into my CAS.

    I get 2 solutions. The approximate values are high-lighted. (Click on the thumbnail to get a larger image)
    Attached Thumbnails Attached Thumbnails An equation that doesn't want to be numerically solved-app_solutions.png  
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  7. #7
    mfb
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    Re: An equation that doesn't want to be numerically solved

    I think the board, WolframAlpha or my browser messed the link up. It came from the correct equation.

    earboths solutions look good: The argument of the logarithm has to be very large, this can be done in two ways: Large 1/(Jp-B) in K1 or large 1/Jp in K2. Those options lead to the posted solutions.
    Something close to 0.9 cannot solve the equation, the argument of the logarithm would be too small.
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  8. #8
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    Re: An equation that doesn't want to be numerically solved

    First of all, I'm very pleased to you for your help.

    What CAS do you use ? Derive, Mathemathica ?
    Thanks.

    Jose
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  9. #9
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    Re: An equation that doesn't want to be numerically solved

    Quote Originally Posted by Pepelu View Post
    First of all, I'm very pleased to you for your help.

    What CAS do you use ? Derive, Mathemathica ?
    Thanks.

    Jose
    I assume that I'm meant(?). If so: In this case I used Derive (the latest version)
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