# Questions tagged [periodic-function]

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### Evaluate the time average of Mathieu functions

I defined a function composed of Mathieu's periodic functions: ...
68 views

### How to constrain a Mathematica vector to a periodic domain?

Consider a function $F({\bf v})$, where ${\bf v}=(v_x,v_y)$ is a vector in $\mathbb{R}_2$. I would like to define a new function $f({\bf v})$ which is periodic under $f({\bf v})=f({\bf v}+(n_x,n_y))$ ...
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1 vote
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### Error in definition of PeriodicBoundaryCondition?

The documentation for PeriodicBoundaryCondition (https://reference.wolfram.com/language/ref/PeriodicBoundaryCondition.html) has: Where it says $u ( x_{target} ) = a + b\ u ( f ( x_{target} ) )$, I ...
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142 views

### Periodic extrapolation out of the domain of the solution of a PDE in two directions

As a prototypic problem ...
• 9,803
451 views

### FEM: periodic solution of 2D Navier-Stokes equations

Let’s consider a horizontal channel with a round obstacle in the middle. ...
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### Interleaving position

How could I proceed to interleave the presented values to obtain the same result obtained by this code? ...
• 9,233
1 vote
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### Plot on the surface of a Torus

I'm trying to plot a system with a variable (or field) $\theta(x,t)\in[-\pi,\pi]$ which is an angle at every position $x$. The positional argument $x$ itself is a periodic coordinate $x\in[-\pi,\pi]$. ...
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1 vote
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### Mathematica doesn't evaluate my Limit expression

I tried to evaluate the following limit: Limit[Sin[x]^n, n -> Infinity] However, Mathematica doesn't evaluate it, and just reprints the original problem: <...
• 21
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### Solving differential equation with periodic variable (poincare section)

I'm trying to make a Poincare section using the code here: ...
324 views

### How to find max and min values

Need to find max and min values like on pic. I am wondering how I could determine max and min values of oscillations ? How could I find these values: My code: ...
• 573
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### How to efficiently implement periodic function to reuse computed values

Assume I have a function f = Function[t, VeryDifficultComputation] But I would like to exploit the fact that the function is periodic to "cache" computations ...
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### How to make a square wave function with controllable period, phase and duty cycle that can work really fast?

I actually need two things: A square wave function that allows me to control its duty cycle, period and phase. It must work fast enough to be evaluated at least a million times per second. For the ...
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1 vote
261 views

### Using Nearest with periodic boundary conditions of a list

Take the list e = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} I want to get the nearest points but with a wraparound condition. So lets say I want to find the 5 nearest ...
1 vote
98 views

### How to pad periodically a cube to be compatible with ListInterpolation?

Context I would like to define a periodic interpolation function on a cube. It seems mathematica's ListInterpolation and the option ...
• 23k
435 views

### Periodic Orbits of the MacKay Map

For the MacKay (Henon action-angle transformation) Map (Mackay 1983): $x_{n+1}=q-\alpha x_n-x_n^2-y_n \\ y_{n+1}=x_n$ with $q, \alpha \in \mathbb{R}$ real parameters I would like to calculate the ...
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### Using Fourier for periodicity and spike analysis

I am trying to look for significant peaks/spikes and periodic changes or fluctuations in about 60 time series of synthetic data. For example, in data1 below, there ...
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1 vote
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### Definition of periodic conditions

I want to define some periodic conditions, for example, describing an ellipse in 2D with periods $p_1$ in $x_1$ direction and $p_2$ in $x_2$ direction. I am frying my brain trying to implement this, ...
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### Using EventLocator to detect periodic solutions in NDSolve

I loop over some systems of DAEs with NDSolve; some solutions are periodic, some are not. When integrating with NDSolve, I ...
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### Periodic function Iteration limit [closed]

I have two main issues. The first concerns Mathematica interpreting the same definition differently based on what I call the function, even though the name never occurs in any other part of the ...
143 views

### FunctionPeriod returns 0 if input trigonometric function have a real phase

I am using Mathematica 10, FunctionPeriod which is supposed to return period of a given function returns 0 if the input trigonometric function have a Real phase <...
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Code is: ...
• 573
1 vote
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### finding fourier coefficient of a parametric curve [closed]

There is a function in mathematica FourierCoefficient for finding fourier coefficients of a periodic function, but it requires the mathematical expression as input. ...
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764 views

### Solution diverges in periodic PDE

Problem introduced in 11.0.1 and persisting through 11.3 Mathematica version 11 introduces PeriodicBoundaryCondition which is very useful in solving periodic PDE ...
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1 vote
464 views

### Periodic boundary condition trick

I'm plotting a curve on a compact space which is having periodic boundaries on the left and right parts. Currently, the code I'm using is working great, but I'm wondering if there's a simpler and ...
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### How to find period of a discrete sequence?

For example, {1,2,3,4,5,6,7,8} has period 1, the base is {1} {1,2,4,5,7,8,10,11} has period 3, the base is {1,2} I ...
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### How to locate the position of a periodic orbit

These are the equations of the dynamical system ...
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