Linked Questions

36
votes
2answers
1k 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 ...
10
votes
4answers
822 views

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 ...
13
votes
3answers
3k 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.
26
votes
3answers
765 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: ...
39
votes
1answer
2k views

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 ...
14
votes
2answers
2k views

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. ...
19
votes
1answer
367 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 ...
9
votes
2answers
628 views

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: ...
11
votes
1answer
780 views

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. ...
10
votes
1answer
2k views

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 ...
7
votes
1answer
1k views

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 ...
5
votes
1answer
930 views

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 ...
6
votes
3answers
339 views

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
votes
2answers
221 views

Multiply integrand with -1, and the precision changes?

"After multiplying the integrand of NIntegrate with -1, the Precision of the output will ...
5
votes
2answers
373 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 ...

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