Linked Questions
37 questions linked to/from Determining which rule NIntegrate selects automatically
48
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2
answers
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How to work with Experimental`NumericalFunction?
This question is intimately connected with previous one: "How to create internally optimized expression for computing with high WorkingPrecision?"
Oleksandr R. correctly states in the comment:
A ...
- 62.3k
39
votes
2
answers
2k
views
How to implement custom integration rules for use by NIntegrate?
How can NIntegrate be extended with custom implementation of integration rules?
This answer of the question "Monte Carlo integration with random numbers generated ...
- 38k
17
votes
3
answers
5k
views
Chebyshev Approximation
Is there functionality in Mathematica to expand a function into a series with Chebyshev polynomials?
The Series function only approximates with Taylor series.
- 295
10
votes
4
answers
2k
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NIntegrate doesn't evaluate
The integral
Integrate[(t^4 x^3)/Sqrt[-t + x], {x, 0, 1}, {t, 0, x}]
(* 512/5355 *)
can be solved analytically.
Trying to apply ...
- 56.8k
28
votes
3
answers
1k
views
Writing functions with "Method" options
I'd like to implement several behaviors for a particular function using a Method option added to the function definition:
...
- 4,341
15
votes
2
answers
3k
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NIntegrate error bound
I am trying to evaluate a highly oscillatory integral using NIntegrate. I fear that due to limited resources (time and/or memory), I will not be able to evaluate the integral to the desired precision. ...
- 163
17
votes
1
answer
5k
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Obtaining an NIntegrate error estimate
Is there a way to extract the error that Mathematica estimates when calculating a numerical integral using NIntegrate?
Internally Mathematica must keep track of ...
- 3,302
10
votes
2
answers
1k
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NIntegrate appears to give incorrect results
I am trying to specify a bivariate probability density function in Mathematica. As a check, I would like to confirm that it integrates to one. Here is the function:
...
- 201
21
votes
1
answer
509
views
How to implement custom NIntegrate integration strategies?
How can new integration strategies algorithms be used with NIntegrate?
This is a different type of extension than the extensions with new integration rules, as ...
- 38k
12
votes
1
answer
1k
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Is there a way to see the result of NIntegrate's symbolic preprocessing?
NIntegrate can do a number of different types of symbolic preprocessing on the integrand before starting the numerical calculations, including changes of variables.
...
- 236k
7
votes
3
answers
589
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Avoiding the suppression of messages by NIntegrate
Consider the following code:
test[x_] := If[1 < x < 2, Message[Test::message]; x^2, x];
NIntegrate[test[x], {x, 0, 3}]
5.33333333333334
I.e. it gives me ...
- 7,182
6
votes
1
answer
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What method does NIntegrate use by default?
There is a variety of algorithms for performing numerical integration (See wiki). What method does NIntegrate use by default?
I looked at the documentation page ...
- 1,155
7
votes
1
answer
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Mathematica 10.2 is slow to NIntegrate highly oscillatory integrals
I noticed that Mathematica V10.2 is taking much longer to run my code when compared with V9. One function that seems affected is NIntegrate. For example, for a ...
- 73
7
votes
2
answers
254
views
Multiply integrand with -1, and the precision changes?
"After multiplying the integrand of NIntegrate with -1, the Precision of the output will ...
- 68.4k
5
votes
2
answers
541
views
Convergence data for Monte Carlo NIntegrate
I am using NIntegrate with Method -> "MonteCarlo" to evaluate a high dimensional integral. Is there a way I can obtain a list ...
- 195