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Jun 20, 2021
08:03 AM

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Jun 20, 2021
08:03 AM

System of Equations - Numerical solution

Hello,

It is possible to find the numerical solution to this system of equations?

(Mathcad 15 File)

Thanks.

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3 REPLIES 3

Jun 20, 2021
08:37 AM

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Jun 20, 2021
08:37 AM

It is possible to find the numerical solution to this system of equations?

In theory, yes, but it might take some effort and thought.

First, you've got four equations in four unknowns, not five in five; your last equation is a definition:

, wugf can be had directly from this equation.

The second problem you have is scale. Coefficients with powers of ten to 26 are going to really challenge the numerical engine. You might try to "rescale" the problem back into more reasonable numbers.

Jun 20, 2021
10:15 AM

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Jun 20, 2021
10:15 AM

You've got 6 equations and 5 unknows. This means there will probably not be a unique solution unless you're lucky.

Let's see:

I've tried it with eq 3 and 5. That results in values for wz1 and wz2. But entering all values in the Left hand segment of eq4 results in a value order 1e9, not anywhere near a few hunderd...

So you have two problems before you can solve:

**1st**: Find an extra parameter to solve for, or drop an equation.

**2nd**: (As Fred mentioned) reduce the dynamic range of your constants. Note that the range of a-values is from 1e13 to 1e26, that's a ratio of 1e13. mathcad works with floating point numbers with a dynamic range of about 1e17. Only the first 4 digits of a[0 can be significant. When looking at the dynamic range of all constants (a AND b), you have 1e26. You're in 9 digits short....

Success!

Luc

Jun 21, 2021
09:42 AM

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Jun 21, 2021
09:42 AM

Search for an algebraic solution: