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How do I find the appropriate Global Adaptive values?

Posted 10 years ago
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The question turns out to only be part of my frustration. I am new to Mathematica but am solving a real but deceptively simple model.

When I use Integrate, I get an enourmous number of terms and conditionals, some imaginary, yet manual integration does not present these alternatives. I need to surpress some of the machinations within Mathematica that are not relevant to my solvution.

When I turn to DIntegrate, after a few terms in an expansion, I get a complex error message. None of my attempts at using the suggestions resulted in an improvement. I asked someone, and he suggested decreasing my accuracy goal setting. This worked whereas none of the suggestions by Mathematica did. The actual error message is below in quotes. 

"NIntegrate::eincr: The global error of the strategy GlobalAdaptive has increased more than 2000     times. The global error is expected to decrease monotonically after a number of integrand evaluations. Suspect one of the following: the working precision is insufficient for the specified     precision goal; the integrand is highly oscillatory or it is not a (piecewise) smooth function; or the true value of the integral is 0. Increasing the value of the GlobalAdaptive option     MaxErrorIncreases might lead to a convergent numerical integration. NIntegrate obtained 0.143967 and 0.0000346605 for the integral and error estimates."
Out[75]= 0.0539877

I included the output because I do not understand how this output is related to the final statement in the quote: NIntegrate obtained 0.143967 and 0.0000346605 for the integral and error estimates. 

I would like someone to point me toward a reference in which I can understand the vocabulary and consequences to implementing a workable solution using Mathematica. If I need to decrease my accuracy, how to I know how much my accuracy is being degraded and by how much?

Regards and thanks for any help.
POSTED BY: Luther Nayhm
3 Replies
Posted 10 years ago
If you can show the simplest example of your integral that generates the enourmous number of terms and conditionals then someone might be able to offer a few suggestions to help get you started.
POSTED BY: Bill Simpson
Hi  Luther,

Have you tried to use "GenerateConditions" and "Assumptions" options for Integrate?
Perhaps this may help to reduce your problem.
Also take a look at "tutorial/NIntegrateIntegrationStrategies" in documentation.

I.M.
POSTED BY: Ivan Morozov
Posted 10 years ago
I will give it a go and report back...sometime. I may abandon Mathematica and try to implement a separate numerical integration algorithm. Learning curve is steep.

Regards.
POSTED BY: Luther Nayhm
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