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 ...
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 ...
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.
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: ...
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 ...
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. ...
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 ...
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: ...
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. ...
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 ...
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 ...
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 ...
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 ...
221 views

### Multiply integrand with -1, and the precision changes?

"After multiplying the integrand of NIntegrate with -1, the Precision of the output will ...
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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