# Tagged Questions

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

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### 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 ...
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### Eigenvalues of large symmetric matrices

When I try to compute the eigenvalues of the adjacency matrix of a very large graph I get, what can be charitably described as, garbage. In particular, since the graph is four-regular, the eigenvalues ...
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### NDSolve and memory usage

After some googling, i've found similar problems around, but didn't find a 100% satisfactory answer, so let me ask here: I'd like to solve a 1+1 problem using the method of lines. In spherical ...
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### Underflow occurring in computation

I've got an "Underflow occurred in computation" problem. Here's a simplified version of the code: ...
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### Rationalize error

The docs state that "Rationalize[x,dx] yields the rational number with smallest denominator that lies within dx of x." However, testing this out it appears to be false. ...
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### A simple syntax does not work

The code below does not work. Can anyone tell me why? Thanks! ...
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### NSolve and FindRoot failing to evaluate

So I am integrating a Piecewise function and then using NSolve to find out where the limits of integration lie to satisfy an ...
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### Incorrect numerical derivative of function that uses FindRoot

I am trying to plot the derivative of function g[x] below where g[x] is defined as the root of another equation. However, I am ...
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### Optimization: Area of solvable constraints

I need some support with the following problem: In a polar-type problem, I hand over a list of variables rlist and a numerical optimization function (e.g. ...
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### Confused by (apparent) inconsistent precision

$$e^{\pi \sqrt{163}} \approx 262537412640768743.99999999999925$$ E^(Pi Sqrt[163.0]) N[E^(Pi Sqrt[163.0]), 35] NumberForm[E^(Pi Sqrt[163.]), 35] returns <...
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### A problem about function N

Toady,I have a problem about N,described as below: For example N[1/3, 5] (* ==> 0.33333*) and ...
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### Error “Summand (or its derivative)…is not numerical at point m = -85.” on a simple sum

I'm a beginner on mathematica.. I'm trying to calculate a simple sum of a function, ...
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### Why FinancialDerivative fails for the Spread case?

According to the documentation center for FinancialDerivative in version 10.4, when there are multi assets, we still may use ...
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### How can I make NIntegrate aware of a singularity along a curve, e.g. a circle in a 3D integral?

I am having some trouble trying to get Mathematica to do a numerical integral over three dimensions which contains a singularity of dimension 1, and I would like some pointers to solid resources on ...
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### Why do these calculations 'stop'? [duplicate]

Question 1: If I change guess to a integer, for example guess = 1 then ListPlot already stops at $n=50$. This seems strange to me, any ideas on why this happens? ...
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### Can I use operators of the form $\frac{d^2}{dx^2}+i\frac{d}{dx}$ inside NDEigensystem?

I am currently trying to find the eigenfunctions of Hamiltonians of the form $\hat H=\frac12 \hat p^2 +a\hat p +f(\hat x)$, and I thought I would give NDEigensystem ...
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### Changing variable in numerical solution

I solved numerically the differential equation: ...
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### Proper way to create plot of equation with parameter solutions

for example I am trying to execute this code: ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Numerical derivative step size

I am trying to perform a numerical derivative of some function using ND. I want to know if there is a way to set the step size of differentiation to the specific ...
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### Chains of approximate numeric equalities

Mathematica considers two numbers equal if "at most their last seven binary digits" differ. For example: ...
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### difference between FullSimplify and Simplify

I have a problem to dinstinguish the following two mathematica codes, the only difference is the first use FullSimplify and the second is Simplify. but the results are totally different. what is wrong,...
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### Using Associations and Pattern matching in numerical functions possibly broken

It looks like the very young feature of pattern matching (/replacing) within Associations (http://mathematica.stackexchange.com/a/119542/6804), with or without ...
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### Numerical comparisons of matrices

I have a matrix which should be equal to a null matrix. However due to the numerical precision, a brutal equality test with a matrix initialized with zeros does not work. How should I perform the ...
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### Finding and plotting a parametric solution to a complicated equation (transcendental, log-polynomial)

I am trying (desperately) to find a way to solve a transcendental equation whose solution $x$ depends on non-numerical parameters $a$ and $b$. And then to produce a ...
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### NSolve and domain specifications

I am using NSolve to find roots to a system of polynomials that describe some chemical reactions. However, I am seeing some odd behavior when I restrict the domain. First, the basic setup: ...
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### Union sorting after ignoring some digits

I have a list with its bellow elements: {-0.7071067811865476, -0.7071067811865475, 0.7071067811865475, 0.7071067811865476} If I use ...
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### Annoying display truncation of numerical results

I have a lot of data to inspect. An example of a number in my program is 123.189094 This gets displayed as 123.189 ...
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### FindMinimum step size too small

I'm running a simulation of an electromagnetic system using Radia, an external code that is run from Mathematica. I want to use FindMinimum to determine some ...
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### How can I do numerical calculation directly without any symbolic calculation? [duplicate]

Here I define a set of functions: ...
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### Machine-Precision and Arbitrary Precision [closed]

What is meant by a machine number in the Mathematica documentation? What is the difference between machine-precision and fixed-point precision? What is arbitrary precision?
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### Evaluation of Element?

What is the Mathematica reasoning behind the result of the first two elements on the second row of the following table? ...