According to the following Mathematica reference
http://reference.wolfram.com/language/tutorial/NIntegrateIntegrationStrategies.html#112801667
I know that
“If it is known where the singularities occur, they can be specified in the ranges of integration, or through the option Exclusions.”
I would like to get to know other methods which can be useful for me. It can be limited to a single integral.
Dear Yiwei,
You suggest very good strategy. The simplest kind of my integral looks like the following
NIntegartion[g[x] Exp[-f[x]],{x,0,1}]
where g[x] can be assumed as x^k and f[x] changes monotonically from 0 to –Infinity.
That implicates Exp[..] changes from 1 to 0. I do not know explicitly f[x] (it is a result from other complex calculations)
I try to evaluate the integral near the singular point directly for example from 0 to 0.99.
Dear Pablo,
Thank you for your interesting example with loop and epsislon. I have just thought about using similar construction (with epsilon), but your proposition extends my idea. I solved the problem but from the other hand the accuracy is less than I expected. I can suppose from the other theory what boundary values can be obtained. Maybe I approximate f[x] and g[x] with less accuracy than it is needed. I use InterpolatingFunction[] to get the values for the discussed integral.
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