# Questions tagged [numerics]

Questions on the numerical functions of Mathematica, implementing numerical methods and numerical computing with Mathematica.

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### When does NDSolve parallelize ODE system solving?

I've long believed that NDSolve cannot make use of multiple cores to solve ODE system, but things seem to be different at least since v12. Consider the following ...
423 views

### What happened to SequenceLimit?

In older versions of Mathematica, there was a function called SequenceLimit that allowed taking the limit of a numerical sequence. It is useful for speeding up the ...
495 views

### Why is my data 10 times slower than random data when doing matrix multiplication

I have some data generated from some program, and it appears that matrix multiplication on these data are about 10 times slower than on some random data: ...
2k views

### How to compute the inverse CDF of HyperbolicDistribution properly?

Fixed in version 9. I want to compute the CDF and inverse CDF of the hyperbolic distribution: ...
5k views

### Parallelizing Numerical Integration in Mathematica

I have an ugly, six dimensional function that I need to integrate numerically. It works, but it currently take twelve hours to complete the calculation. Is there any good way to parallelize the ...
3k views

### Numerical partial derivative

For a one-variable numerical function, it's simple to calculate the derivative at a point with Derivative as Szabolcs has pointed out before: ...
296 views

### How does Plus work on machine precision Real arguments?

I thought Kahan's summation method would make a nice example for students to use to think about round-off error [W. Kahan, Pracniques: Further Remarks on Reducing Truncation Errors, Commun. ACM 8  (...
5k views

### Does Mathematica get Pi wrong?

I happened to watch a Youtube video on Pi. According to the video, the 1 millionth digit of Pi is 1. And here is another page of the first 1 million digits of Pi. You can get the same answer from ...
488 views

### Make mathematica treat $e_i^2$ as numeric

With NumericQ[symbol] = True, I can declare that a symbol is numeric. I want the expressions matching: $$e_{\text{i\_}?\text{IntegerQ}}^2$$ to be treated as ...
1k views

### How do I numerically evaluate and plot the Fabius function?

The Fabius function is a well-known example in analysis of a non-analytic function that is infinitely differentiable. I want to be able to numerically evaluate the function for any real argument, as ...
602 views

### Why is MainEvaluate being used when LinearSolve can be compiled?

According to this question LinearSolve can be compiled. However, CompilePrint[] shows a call to ...
3k views

### more numerically accurate inverse matrix

I encountered the following matrix mat = {{2, 2.161209223472559 + 1.682941969615793 I}, {2.161209223472559 - 1.682941969615793 I, 2}} and ...
2k views

### Poisson solver using Mathematica

I am looking for some help with a Poisson solver I am writing in Mathematica. The code is quite long with Arrays plugged in, so the full details can be found at http://pastebin.com/uSrSDcW6 I am ...
2k views

### ParallelEvaluate for function minimization

Is there a parallelized version of a minimization routine available in Mathematica? The objective function is non-linear and the gradients have to be numerically computed. Every function evaluation ...
2k views

### Is it possible to use the LevenbergMarquardt algorithm for fitting a black-box residual function?

I have a black-box multiargument multiparametric function of the type SRD[dataPoint_List,params_List] which accepts experimental data along with the parameters of ...
486 views

### RandomReal closed on left & open on right?

I have a number of algorithms that depend on uniform random reals in half-open intervals such as $[0,1)$. In particular, I need a (pseudo) random-number generator that produces machine-precision ...
660 views

### Why do NumberForm and Round apparently use different tie-breaking methods?

When rounding numbers (for example, rounding a real number to the nearest integer), the "round to nearest" rule is usually used. For example, 1.4 is rounded down to 1 and 1.6 is rounded up to 2. ...
2k views

### Numerical evaluation of a sum

I am trying to compute numerically NSum[(-1)^n/n^3, {n, 1, Infinity}]. Of course, using first Sum would work here, but often it'...
503 views

### Can Mathematica provide a reliable estimate of the numerical error from NDSolve?

In the Details section of the Mathematica documentation for PrecisionGoal, one is told that Even though you may specify ...
2k views

### Strategies to avoid LessEqual::nord in NMinimize?

When using NMinimize on functions with complex intermediate expressions (but a real end result), quite often one gets the error ...
533 views

### Terrible accuracy of DawsonF

DawsonF[30.] returns 0. The correct value is 0.016676... At least it prints a warning message, ...
7k views

### Numerically obtaining the inverse Laplace transform of data

I have been using several Mathematica packages to do numerical inverse Laplace transforms on known (expressible in closed form) expressions, $\tilde{f}(s)$. I am now being confronted with the more ...
475 views

### “ParametricSensitivity” in ParametricNDSolve

"ParametricSensitivity" is listed as a Method in the documentation for ParametricNDSolve, ...
775 views

### Non Standard Eigenfunction Plots of the Laplacian Over the Unit Square

I have recently been plotting eigenfunctions of the laplacian over the unit square using the NDEigensystem command. However, I have noticed something in the plots ...
936 views

### Converting to machine precision

There are multiple ways to convert an expression to machine precision, for example: ...
723 views

### Jacobian of ParametricNDSolve and FindRoot for the Three Body Problem

The main problem I took the time to reformulate the question in a more appealing and concise way. I want to find bifurcations of solutions to the three body problem. In order to do that, I define ...
227 views

### How is the Hessian computed using ExperimentalNumericalFunction?

Here and here it was explained how to use ExperimentalNumericalFunction to compute the Hessian of a numerical function. I would like to know how this undocumented ...
271 views

### Bug? Numerical calculation error with FullSimplify and arbitrary precision

Bug introduced after 5.2, fixed in 8.0, reintroduced in 9.0 and persisting through 12.1 Is this a bug? If I do FullSimplify[n E^(010 n)] then it returns <...
1k views

### Why is Poisson Random Deviate Generation so slow?

I am generating Poisson deviates for some numerical work. Mathematica 9.0.1 is very slow in generating these random numbers, as can be seen below. ...
814 views

### Is there a faster way to calculate Abs[z]^2 numerically?

Here I'm not interested in accuracy (see 13614) but rather in raw speed. You'd think that for a complex machine-precision number z, calculating ...
989 views

### NDSolve DAE with Constraints

I'm trying to make some numerical simulation with NDSolve. I have encountered a few problems. Here is a simplified version of the equations: ...
263 views

### Keep Round-Off errors for educational purpose

I want to show examples of round-off errors in some numerical algorithms to my student, in order to motivate the study of algorithms with a better behavior. While it is easy in any other language, I ...
1k views

### Water Hammer - Numerically solving system of PDEs

I'm trying to use Mathematica to solve the water hammer effect. ...
130 views

### Apply N only outside a certain function

1 + f // N gives 1. + f[1.] I don't want the argument of f evaluated by N; I ...
491 views

I'm trying to find the following limit using Mathematica: $$\lim_{N\to\infty}\sum_{k=1}^N\left(\frac{k-1}{N}\right)^N$$ The problem is taken from here and is known to converge to $\displaystyle\frac{... 1answer 1k views ### How trustworthy is NMaximize? Suppose I solve a constrained optimisation problem using NMaximize. How confident can I be of the accuracy of the result? For concreteness, suppose that F,G are (... 2answers 11k views ### How do you force a decimal output? [duplicate] I have some very small values such as 2.601519253*10^-8. I'd like to output these values to CSV for another program to work with. I've tried N[value, 50], but Mathematica still insists on producing ... 1answer 4k views ### Kramers-Kronig relations I am trying to calculate the change of the refractive index from the change of the absorption coefficient using the Kramers-Kronig relations, in Mathematica. ... 1answer 493 views ### Does NRoots own an abstract counterpart? If not, can we write one? We know when solving linear algebra equations, despite its abstract syntax, LinearSolve is much faster compared to Solve: ... 1answer 175 views ### A weird issue with Interval[$MaxNumber]

Bug introduced in 9.0 or earlier and persisting through 11.0.1 or later From the Interval documentation: For approximate machine- or arbitrary-precision numbers ...
2k views

### Trying to find the asymptote to a function

I am trying to find the asymptote to a solution of a differential equation. I solved $x'(t) = \sin(x(t) + t)$ using NDSolve and plotted my solution. ...
505 views

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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. ...
5k views

### Is Abs[z]^2 a bad way to calculate the square modulus of z?

For a numerical quantity z, Abs[z] returns the square root of the sum of the squares of the real and imaginary parts of ...
773 views

### Why does 1 - Exp[-10.0^12] cause an out-of-memory error?

I would like to understand why evaluation of the expression 1 - Exp[-10.0^12] causes an out-of-memory error and how can I prevent such errors when calculating ...
408 views

### Wrong computation with N

I was trying to solve this problem using Mathematica 8.04. I did this: ...
4k views

Finding a global minimum for this problem (non-linear optimization by the Nelder-Mead downhill simplex method) may not be possible, but by finding local minimum, I am expecting the value of the ...
431 views

### SymplecticPartitionedRungeKutta shows strange error

Bug introduced in 9.0 and fixed in 11.3.0 or earlier I tried to solve Hamiltonian system ($Q$ is a vector of all generalized coordinates, $P$ - of generalized momentum)  \frac{\mathrm{d} Q}{\mathrm{...