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# Questions tagged [numerics]

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

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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....
60 views

### Testing the accuracy of numerically computed derivatives

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

### More elegant/efficient numerical WKB implementation for 1D Schrödinger Equation

I'm trying to figure out a better way to implement numerical WKB quantization of a spectrum. WKB quantization is the condition that $$\oint_{E}p \, \mathrm{d}q = \pi \hbar (n+1/2)$$ So the idea to ...
57 views

### Allow Mathematica to solve the differential equations with larger than 16 digits parameters

Consider the system of differential equations ...
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### Numerical maximization

I am facing a numerical maximization problem with constraints. Using Method -> {"RandomSearch", "SearchPoints" -> 3}, AccuracyGoal -> 2 often does not find ...
109 views

### Find the square root using a recursive formula [on hold]

I want to approximate the square root x=Sqrt[a] for $a>0$ using the the formula $x_{n+1}=\frac{1}{2}(x_n+a/x_n)$. How can I do this?
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### Power towers Power towers from x to n [on hold]

How can I make Mathematica calculate a power tower for a succession of numbers, but instead of writing them, Mathematica does the iterative calculation. ...
26 views

### Constrain values to numeric during Minimize

I understand, that similar questions have been asked before, but I am absolutely new to Mathematica and can not solve it myself: In nuce it is the following: I want to calculate ...
489 views

### Morphing between two functions

Assume we have 2 peaked positive functions f[x_] := Exp[-(x + 3)^2] g[x_] := 1/2 Exp[-(x - 3)^2/4] that look like Would it be possible to numerically find a ...
354 views

### How to calculate an infinite sum to 100 exact digits with NSum?

In the discussion https://math.stackexchange.com/a/3419778/198592 I stumbled of the question how to calculate the sum $$s= \sum _{n=3}^{\infty } \frac{n \cot \left(\frac{\pi }{n}\right)}{4^{n-2}}$$ ...
229 views

### How to evaluate theta function's derivative numerically?

I run into this derivative but Mathematica won't evaluate: ...
193 views

### Solving a steady-state viscous Burger's equation with NDSolve

A steady-state viscous Burger's equation is given by $$u\,u'=\nu \,u'', \quad x\in (-1,1),$$ $$u(-1)=1+\delta,\quad u(1)=-1.$$ Here $\nu>0$ is the viscosity, $\delta>0$ is a small ...
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### Efficient way to list zeroes of an oscillating function

From "The First 50 Million Prime Numbers" by Don Zagier: primes are integral roots of$$1-\frac{\sin(\frac{\pi\Gamma(s)}s)}{\sin(\frac\pi s)}.$$ The graph of this function looks like I would like to ...
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### “Arnoldi” method for Eigenvalues inside FindRoot

I'm trying to implement a function which, given a matrix with one free parameter, would return the value of the parameter at which the lowest eigenvalue of the matrix is equal to a certain number. ...
31 views