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.

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.

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.

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

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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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)

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.

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

Re: An equation that doesn't want to be numerically solved

Quote:

Originally Posted by

**Pepelu** 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)