Questions tagged [error-propagation]

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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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1answer
100 views

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 ...
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3answers
504 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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2answers
54 views

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% ...
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1answer
71 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}];
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How to put error bar in data, in Loglinear scale?

I have to put error bars and (have the idea of Chi-square) in experimental data with fitting on a log-linear scale. But all the available resources failed to achieve this. I used this code ...
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3answers
156 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 ...
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1answer
139 views

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 "...
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1answer
154 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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1answer
122 views

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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2answers
101 views

Testing the accuracy of numerically computed derivatives

I am calculating approximate derivatives by using NDSolve`FiniteDifferenceDerivative, so this works: ...
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1answer
223 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 ...
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1answer
128 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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1answer
37 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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1answer
308 views

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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3answers
1k views

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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2answers
387 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 $(x_i,y_i)$ ...
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1answer
66 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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2answers
468 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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1answer
144 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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58 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-...
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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 ...
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2answers
301 views

Error propagation in finding full width at half maximum

I have an equation given by: ...
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0answers
75 views

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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1answer
378 views

Propagate error through `FindFit`

I have several sampled points $(x_i, y_i)$ with mutually independent error on the y coordinate $\sigma_{y_i}$. For simplicity, I'm assuming no error in the x coordinates ($\sigma_{x_i} \ll \sigma_{...
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129 views

Determining the intersection of two functions with errors on parameters

Let's assume I want to calculate the intersection points of two functions $f(x)$ and $g(x)$. That is simple enough, I define my functions, e.g. like so and use Solve...
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2answers
877 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 ...
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131 views

Error propagation with NDSolve and periodic boundary conditions

I'm trying to solve the problem of heat conduction through soil with periodic temperature variations on the surface. For now I'm working with a 1D model but I see that the solution doesn't work, it ...
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2answers
1k views

Error propagation code

I have a code for error propagation :- ...
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4answers
1k views

Create an adaptive amount of local variables for error propagation

I intend to write a function which calculates the result and the error for any formula with any amount of variables using the Gauß Error Propagation. The error $\mathrm{d}R$ for a function $A(a,b,c)$ ...