# Questions tagged [error-propagation]

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### How to isolate uncertainty in formula involving Around[]

If I compute with Mathematica Exp[Around[v, dv]] //PowerExpand I get Around[Exp[v], dv*Exp[v]] with the uncertainty ...
• 324
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### Around with multiple errors

To my knowledge, Around only deals with one error. That means it can't deal with multiple sources of errors. For example, a number may have both statistic ...
• 988
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### Correlated uncertainties

navigating through the docs. of Around one can read in the details that When Around is used in computations, uncertainties are by default propagated using a first-...
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### How to copy a number from an error message? [duplicate]

Is there any way to copy a number from an error message and assign it to a variable, without manually doing it? For instance, I am trying to solve some coupled Differential equations as follows: ...
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### Around error propagation

I understand that when Around is used in computations, uncertainties are by default propagated using a first-order series approximation, assuming no correlations. On the other hand this makes it ...
537 views

### Mathematica 12.x: Don't use Accumulate or Differences on Around objects!

Bug introduced in 12.0 or earlier and persisting through 12.2 or later It seems we've discovered a bug! The following is a summary of the problem and possible workarounds. Scroll down to ORIGINAL ...
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### Relative error with bands plot

I have 2 sets of data imported from excel file, Let say A = 20 21 22 ... 30A B= 0 1 2 3 ... 10 I want to plot A with a relative error of 10% ...
73 views

### plotting error in 3D

What is the problem related to the following plot? Definition of geometry RR = ImplicitRegion[((Sqrt[x^2 + y^2] - 9))^2 + z^2 <= 1, {x, y, z}];
217 views

### Higher order Around, for large error propagation

TLDR question: How to redefine Around to work with higher order approximation. Motivation From the documentation Around ...
• 28.9k
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### Half-absorbing boundary conditions

I'm trying to solve the spherically symmetric wave equation $$0 = (\partial_t^2 - \partial_r^2 + 1)\phi(t,r)\,,$$ where $\phi(t,0) = 0$. Without doing anything fancy, we can solve this equation "...
• 223
225 views

### Estimate errors during integration of interpolated data

I am interested into calculating the errors associated with an integration over interpolated data. Suppose I have something like this: ...
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### Testing the accuracy of numerically computed derivatives - alternative method

So I have asked this question earlier today: Testing the accuracy of numerically computed derivatives, This method works well for DifferenceOrder methods but upon reading https://reference.wolfram....
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1 vote
119 views

### Testing the accuracy of numerically computed derivatives

I am calculating approximate derivatives by using NDSolveFiniteDifferenceDerivative, so this works: ...
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353 views

### How to find the Maximal Absolute Error?

I found this fit but I do not understand how to find the maximal absolute error nor do I understand what it is really. I do not see what it is I would compare, would it be ...
204 views

### Properly defining and plotting a function that requires NSolve

I want to defined a function that solves some equation numerically: ...
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39 views

### Error of a function containing complex numbers

Please, what is the statistical error formula of the function f (uncertainty) by Mathematica code: a=x+I y ; b=u+I v; f=Abs[a]^2+Abs[b]^2;
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### How to get an absolute value of Around?

Around is a useful feature of Mathematica 12 to work with uncertain data. x = Around[-1, {0.5, 1.5}] $-1.0^{+1.5}_{-0.5}$ ...
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### How does the Around command at zero work?

I enter: Around[0,0.5]^2 and I get 0. This is a bit strange. Around[0,0.5] is supposed to represent numbers between -0.5 and 0.5. So by my estimates the square ...
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1 vote
535 views

### Estimating the uncertainty in the slope of a straight line given the uncertainty in the data points

Basically I have some datapoints on the form $(x_i,y_i)$ ...
• 159
1 vote
67 views

### Error propagation with complex number [duplicate]

I have an expression of a physical observable in which some input parameters are taken. The corresponding errors of these input parameters are given. To get the error of this observable what code I ...
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511 views

### Around usage results

Why is Around[10, 1]^2 +- 20 and Around[10, 1] Around[10, 1] giving 100 +- 14 ? Just curious I would suspect them to ...
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151 views

### Why does Success[...][key] work and Failure[...][key] doesn't work?

I'm trying to figure out what is a quick way to add error reporting to my user defined functions. I was experimenting with Success and ...
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62 views

### Error plotting in 2D

I have some data: along Y axis: 5.86*10^(-8),2.56*10^(-8),3.21*10^(-8) with error 0.58, 0.25 and 0.32 respectively. along X axis: there are some range corresponding each value of Y axis such as: 0.1-...
56 views

### error bar plotting with some range

In the following pic I want to show the error bar plotting with some given data: Y axis: 5.86*10^(-8) with error .58*10^(-8) and X axis: 0.1 to 2 (that means there is a range), 2.56*10^(-8) with error ...
1 vote
418 views

### Error propagation in finding full width at half maximum

I have an equation given by: ...
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### How to use "Chop" kind of operation on whole mathematica file

In an array of steps including logarithms and integrations, I am finding the problem of small imaginary parts of some o/p's which are complicating/inhibiting the further steps. I found that "Chop" ...
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