# Questions tagged [numerical-value]

Question relating numerical representations, operations and methods, including approximate results instead of exact symbolic results.

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### GroupBy twice gives different results

Bug introduced in 7.0 or earlier and persisting through 11.1 It took me quite a lot of time to finally trace down to this strange output. I really don't know why. First, I create a list ...
825 views

### Error and uncertainty propagation: Is using Precision/Accuracy a sound strategy?

Questions What are the available resources to deal with experimental error and uncertainty propagation in Mathematica? Given that Mathematica already uses linearized model of error propagation on ...
2k views

### Solve Laplace equation in Cylindrical - Polar Coordinates

Hey mathematica stackexchange!! I've got a (possibly stupid) problem. I've tried many things to no avail, and I've read every post I've found on Laplace's equation. Background: I'm trying to find the ...
855 views

### What is the fastest way to compute digits of $\pi$ using Mathematica?

There are a lot of ways to calculate digits of $\pi$ using Mathematica. The most naïve way I can think of is N[π, 100000000] Of course, there are a lot of fast ...
516 views

### Matching pair of numbers {a,-a}, where a is numeric

Imagine you have a list of pairs of numbers, such as {{2,-2}, {1,5}, {1,-3},{-3,3}} The task is to reduce the given list to a list of pairs of type ...
2k views

So, I was doing some calculations in Mathematica, and came across the following paradox! (I may be exaggerating, but...) I wanted to solve the following equation: $3.33333*10^{-15} - 3.33333*10^{-15} ... 2answers 3k views ### Could I define 0^0 to be 1? [duplicate] Many occasions, where I need to work numerically with functions. For a variable strictly between 0 and 1, during the optimization, it could become 0.^0 or 0^0, which then become indeterminate. Is ... 2answers 366 views ### Why does N[Re@f] give complex result? Consider this code: ... 2answers 350 views ### how to get single, and quad Precision out of Mathematica which match Fortran result by default, if a number has decimal . after it, then Mathematica will do computation using machine Precision, which on my PC (intel hardware) running windows 7 64 ... 4answers 139 views ### Suppress trailing 0s in numerical values For example, this is what I want In:= N[Table[4^(i/4), {i, 1, 4}]] Out= {1.41421, 2., 2.82843, 4.} But if I want a few more digits only from the irrational ... 1answer 169 views ### Machine precision infinity Is it possible to obtain the machine precision (double) version of Infinity? This is useful when using LibraryLink and C ... 3answers 242 views ### How to plot output data of Do-command? The following in a simple numerical solution of the simple harmonic oscillator. ... 3answers 131 views ### Different Methods in NIntegrate I am trying to numerically calculate a multidimensional integral which involves Jacobi elliptic theta functions. The integrand is the following: ... 3answers 327 views ### How to complete function which is not defined for all interval I have a function testF22 like this ... 1answer 104 views ### N[Product] and NProduct give different results I have some trouble. I've been using finite product to study a certain function (see below). However, when I wanted to compute it precisely, I decided to use ... 0answers 344 views ### How does NSolve find the roots to an equation? I'm using NSolve to find the roots to a transcendental equation. For this, I need to specify a bounded region where roots are searched. What I want to know is how <... 1answer 340 views ### DensityHistogram label/display values in Mathematica 8 I'm trying to make a DensityHistogram in Mathematica 8 that overlays the histogram values for each location. What I want is for the value of each square to be ... 1answer 123 views ### 1-D PDE with nonlinear ODE as boundary condition Recently, I am trying to solve a 1-D PDE with a nonlinear boundary condition using the function NDSolveValue. However, it seems that MMA (12) cannot solve it directly with some computational issues. ... 2answers 213 views ### Torus-geometry algebraic equations using NSolve and Reduce Somehow a set of naive-looking equations cannot be solved by using NSolve. Mathematica returns a message like this: ... 1answer 115 views ### Why does this test yield True I have this test implemented in my code, when I import a numeric matrix, which I thought would be bulletproof, but it's failing in this case: ... 1answer 718 views ### Fixed-Point Numbers in Mathematica I am working with a library that needs input in a Fixed Point notation. I’d like to figure out a way to convert the floating point results into fixed point representation. The fixed point length is ... 1answer 609 views ### What does it mean that “there are no significant digits to display”? [closed] So I substitued with the following values in my function T(x,n) and it gave me this red box with the value in the picture. When I hover over it, it tells me that there are no significant digits to ... 2answers 578 views ### How to obtain numerical solutions of a two-variable equation? I have a two-variable function: f[x_, y_] := (4 y^2 - 6) (Cos[y π] Cos[x] - Cos[2 y π] Sin[x]) How can I find all the numerical solutions for$x$and$y$such ... 2answers 656 views ### Mathematica will not solve this numerical equation I have the following equation: ... 1answer 547 views ### Recognize physical constants? Is there some way to ask Mathematica to recognize physical constants, such as 32 or 9.81 (gravitational acceleration, in different units, at Earth's surface)? I have in mind something like the "... 2answers 292 views ### Visualizing the Schrödinger equation for dipole based interaction Hamiltonian I want to evaluate and plot the solutions of coupled linear differential equations. For each time frame, I want to display the probability values (corresponding to mod square of these solutions), and ... 2answers 468 views ### Solving an equation approximately I have a complicated equation in terms of$\omega$and$\kappa$: ... 2answers 191 views ### NIntegrate on a solution of a matrix ODE I've seen similar questions on this site but somehow the solutions there didn't manage to solve my specific problem. I have a function mat1 that takes a square$n \times n$matrix G, and some final ... 2answers 350 views ### Creepy numerical artefacts of a closed-form solution I'm wishing you a nice day and here is my problem: I tried to obtain relation between chemical potential and temperature in a semiconductor and I arrived at this equation: $$2 e^{-\Delta/kT} \left( ... 2answers 157 views ### Solving Equations with HeavisideTheta Functions I need to solve an equation that involves the HeavisideTheta[] function, but regardless of the method I use Mathematica returns an error message. For example, <... 1answer 116 views ### Comparing exact expressions vs real numbers Often I need to generate some data using some symmetry operations and I usually keep them as exact expressions (for example, consider the points on a triangular grid ... 1answer 50 views ### NumericQ and unknown number of variable in a module-block I have the following problem I want to address in an elegant way. I have a function of many variables f[x, y, z,...] I want to find the minimum with ... 3answers 223 views ### How to change random values in manipulate? I made a Manipulate box that is working very well, using lots of random numbers. I would like to add a button to "reset" (i.e. to change, randomize, or reselect) all the random parameters. Here's ... 1answer 102 views ### Laplace equation DirichletCondition ignored My goal is to find out force between two parallel identical disks with Voltage difference. To solve this, I tried to use laplace equation. And below is my code. where R is radius of disks, d is ... 2answers 257 views ### How can one generate an open-ended sequence of low-discrepancy points in 3D? I'd like a low-discrepancy sequence of points over a 3D-hypercube [-1,1]^3, but don't want to have to commit to a fixed number n of points beforehand, that is just see how the numerical ... 1answer 87 views ### Proving the positive semidefiniteness of a 6X6 symbolic matrix Specifically, I want to check the positive semidefiniteness of the following 6X6 symbolic matrix ... 1answer 150 views ### How to avoid rounding error, when exporting numerical values How to avoid the rounding error, when exporting data like this: ra = Range[0.004, 0.074, 0.0005]; Export["range.txt", ra] The result is this: 1answer 151 views ### Inverse prediction function I am trying to write a code which learns a data set. Now, I want to know the input value for a given output value. Consider, the following code ... 1answer 64 views ### How to use NDSolve to solve 1+1 D heat equation u_t=u_{xx} with -\infty<x<\infty and 0\leq t\leq T? How to use NDSolve to solve 1+1 D heat equation u_t=u_{xx} with -\infty<x<\infty and 0\leq t\leq T? ... 2answers 79 views ### Checking NDEigensystem Results I'm looking to verify the output of a call to NDEigensystem. I'm doing this by plotting the operator acting on the Interpolating Function outputs versus the ... 1answer 181 views ### Mathematica and IBVP mixing temporal and spatial derivatives The following PDE's-system-solving code ... 1answer 87 views ### Numerical precision problem I have this simple code: ep = 1 - 80000000000 (-(199999/200000) + 1/E^(1/200000)) ep // N -8.27404*10^-8 ... 1answer 139 views ### Why does NSolve give different results in different version of Mathematica? I am working on a problem with a colleague who uses Mathematica v.10.2 while I have v.11.0 Student Edition. We are solving the exact same equations but get two slightly different results. Why would ... 2answers 605 views ### Plot numerical solutions for a varying parameter I would like to solve this equation \log{\frac{a}{1 - a}} + b (1 - 2 a) = 0 letting varying the parameter b in \lbrace 0,1,\ldots,20\rbrace and then plot the result. I am trying writing the ... 2answers 132 views ### Role of Accuracy in numerical evaluations, SplitBy vs GatherBy This is a follow-up question to this question. I generated a list by substituting the results of a solve[] routine and set: ... 1answer 94 views ### Is this bifurcation or numerical error? I encountered a definite integral (with parameter k) that produces the "chaotic" figures below.$$F(k) \equiv \int_{\theta_k}^{\theta_{k+1}} f(\theta, J \sin\theta - k)\,\mathrm{d}\theta~, \qquad f(... 1answer 80 views ### Numeric values for MinkowskiQuestionMark Why NumericQ[MinkowskiQuestionMark[Pi]] returns False? Is it defined only for algebraics? Numerical evaluation gives some number,... 1answer 127 views ### Solve a system of 4-th order polynomial equations (numerically) I have a function defined on$ S^6 \times S^6 $(two spheres embedded in$ \mathbb{R}^7 $individually). Let us call this vector$ \vec{f}(\vec{x},\vec{y}) $, where$ \vec{x} $and$ \vec{y} \$ are ...
Consider following expression: $$\sqrt{-\left(2 \sqrt{x^{-8/3}-x^{-4/3}+1}\, x^{4/3}+5\right) x^{4/3}+4 \sqrt{x^{-8/3}-x^{-4/3}+1}\, x^{4/3}+2 x^{8/3}+5}$$ In code: ...