Numerical error

[DaveWooff]

Hi all,

I'm using Mathcad 2001i (as part of a Open University course) and have hit a problem. I was wondering if anyone would care to take a look and see if it can be easily resolved. I've attached the doc.

Basically I'm trying to find local maxima and minima of an expression. The expression itself is generated partly numerically but if I copy the expression using manually entered coeff values with the "same" values, I don't experience a problem. I've put the latter case on the second page down in the doc. Hopefully it's not too difficult to fathom.

I know the maxima and minima exist because I can see them on the graph plots (also illustrated).

Regards,

Dave W.

[MikeArmstrong]

Hi David, welcome to the forum.

What course are you studying at the Open University. I completed the Structural Integrity module from the Engineering degree last year.

Mike

[DaveWooff]

Hi Mike,

thanks for the welcome.

Mathematical Modelling MST209. Actually I've finished (and passed!) now so I'm contemplating my next move. Still badly bruised though. It was quite heavy going.

Thanks,

Dave W.

[LucMeekes]

Hi David,

My Mathcad 11 gives 0.566202034099714 as answer for the first (upper, marked yellow) root.

The second (lower, also marked yellow) root results in 0.566202034099816

With the first difference on the 13th significant digit I think that's sufficiently equal.

What values do you see in Mathcad 2001i?

Luc

[DaveWooff]

Hi Luc,

it's helpful to know that a different version of Mathcad is able to deal with it. I get a convergence error - on the first yellow highlighted derror().

Is it possibly a limitation of an old version of Mathcad do you think?

Ta, Dave.

[RichardJ]

What do you have TOL set to?

Does this help? Values for MC11 and MC15 are both for TOL=10^-3.

[DaveWooff]

Hi Richard,

yes I think this solves my problem. So, what is going on? Is your modification something to do with forcing symbolic rather than numerical differentiation?

I had TOL set to 0.001 (default value). Changing the value of TOL didn't seem to have much of an impact unless I set it closer to 1.

Thankyou very much,

Dave.

[DaveWooff]

Actually, I see it now (should have been obvious since you highlighted it for me). Thanks again.

[RichardJ]

I'm not sure what you are referring to, since I highlighted everything I changed.

Yes though, it seems it did not like the combination of a numerical derivative and the numerical root finder. I guess they improved that in later versions.

As a side note, in Mathcad 15 the MuPad symbolic processor understands lsolve, so there is no need to rewrite the solution of the system of equations as matrix math. The Maple engine in earlier versions unfortunately does not understand it, which is a pity because the LU decomposition algorithm used by lsolve is numerically more stable that simple matrix inversion.