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

• Jul 7th 2012, 07:39 AM
Pepelu
An equation that doesn't want to be numerically solved

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

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

I will be very gratefull to you.

Pepelu.
• Jul 7th 2012, 08:05 AM
mfb
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.
• Jul 7th 2012, 08:44 AM
Pepelu
Re: An equation that doesn't want to be numerically solved

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.
• Jul 7th 2012, 08:46 AM
Pepelu
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
• Jul 7th 2012, 08:54 AM
Pepelu
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 ?
• Jul 7th 2012, 09:54 AM
earboth
Re: An equation that doesn't want to be numerically solved
Quote:

Originally Posted by Pepelu
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)
• Jul 8th 2012, 04:44 AM
mfb
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.
• Jul 9th 2012, 12:14 AM
Pepelu
Re: An equation that doesn't want to be numerically solved

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

Jose
• Jul 9th 2012, 06:31 AM
earboth
Re: An equation that doesn't want to be numerically solved
Quote:

Originally Posted by Pepelu

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)