Questions tagged [discontinuity]
Tag for issues caused by discontinuity (e.g. Boole, Piecewise, UnitStep, If, etc) in arithmetic function.
105
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FunctionContinuous for a function defined with Which
The function:
f[x_] := Which[0 <= x < 1/2, x^2, 1/2 <= x <= 1, x^2 + (x - 1/2)^3];
is continuous on the interval $0 \leq x \leq 1$, as a simple ...
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How to include impulses in differential equations?
I have two coupled differential equations as follows:
$$S'(t) = - \frac{a}{1 + B(t)} S(t),$$
$$B'(t) = \frac{c}{1 + S(t)} B(t) (1 - B(t)) - d B^2(t) \Big( \frac{1 - B(t)}{B(t)} \Big)^n,$$
where $a$, $...
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1
answer
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Machine overflow when defining boundary conditions
Recently I have been trying to code Maxwell's equations over a closed surface and have been facing some trouble defining the boundary conditions for the magnetic field.
The equation for the normal of ...
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2
votes
2
answers
78
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Numerical solution of a nonlinear PDE that develops a growing piecewise linear region
I am trying to improve the numerical solution of some PDEs that develop a piecewise behavior during their evolution. The simplest example of one such PDE is for a function $u(t,x)$ with $t \in [-T,T]$ ...
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votes
1
answer
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VectorPlot "Part 1 of {} does not exist" error
Bug introduced in 7.0, persisting through 13.2.
I am looking to plot the Magnetic Vector potential, A, as a function of position along the edge of a density plot. The density plot is fine, and I ...
- 135
3
votes
1
answer
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Why does contour plot not show point(s) where function has a discontinuity?
Consider the following code, which defines a function with a discontinuity, and then generates a contour plot when the function equals that discontinuity.
...
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1
answer
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Solve computes discontinuous eigenvalues of parameter-dependent matrix
So I have a family of unitary matrices $m(x,y)$, which depend on two parameters $x,y \in [0, 2 \pi)$. Its eigenvalues should be continuous in $(x,y)$. Since $m(x,y)$ is a unitary matrix, its ...
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Piecewise Boundary Condition for axisymmetric heat equation [duplicate]
I'm trying to solve the 2D axisymmetric heat equation, where only one section of the tube is being heated up. I have written the following code below:
...
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1
answer
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Discontinuous ODE results in NDSolve::ndinid warning, initial condition is not in the range specified by the discrete variable (internal variable)
The equations and code are below.
The short version is:
I know the error is because NDSolve is doing something in the background to handle the discontinuous ODE. ...
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1
answer
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CaputoD of (Edge) BSplines
tl;dr Why does this works:
CaputoD[BSplineBasis[{3, {0, 1, 2, 3, 4}}, 0, x], {x,
1/2}] // Simplify
Whereas this fails
...
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2
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NDSolve with piece-wise function and BVP
How to numerically solve a system of differential equation with boundary conditions and piece wise affine functions ?
Consider the following system of differential equations from some optimal control ...
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1
answer
116
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How to plot the derivative of a piecewise discontinuous function (by excluding discontinuity points)?
With the following code I am trying to get a plot for the derivative of the ftot1 function, which is a piecewise discontinuous function defined as the sum of other two piecewise discontinuous ...
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votes
1
answer
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How to get $(1-x^2)^{1/2}\theta(1-x)$ continuous?
The function $f(x)=(1-x^2)^{1/2}\theta(1-x),$
where $\theta(x)$ is the Heaviside function, should be a continuous function for $x\geq-1$. Another way to define the same function is,
$$
g(x)= \begin{...
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votes
1
answer
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NDEigensystem: 1D problem with discontinuous coefficients
I am trying to use NDEigensystem to solve the 1D problem
-cs[x]^2 vx''[x] = w^2 vx[x]
with vx[x] and w the eigenfunction and eigenvalue. The coefficient cs[x] is discontinuous at x = -xp, +xp and vx[x]...
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Parts of a Piecewise Matrix Function in NDSolve
First time posting.
Reproducing the Problem
I'm relatively new to Mathematica (using v.12.3), and working on a project. My problem can be reproduced with this.
...
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0
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Numerical solution for multi-step PDEs
I am trying to numerically solve the following PDEs in MMA (v12.0)
$$\partial_u f(x,u) =
\left\{\begin{matrix}&-a f(x,u) + b \, \partial_x^2 f(x,u), & 0<u<T\\ &r(x;\alpha_1) \, f(...
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3
answers
485
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Jump discontinuities in Mathematica
I would like to find discontinuities of the first kind of the function:
Floor[x*Floor[x*Floor[x]]] = f(x)
given a specific interval. For example: how to compute ...
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3
answers
521
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3
votes
1
answer
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How to express a periodic piecewise linear function in terms of Mod function? or linear combination of Mod?
I am programming a small game (with other programming language) in which I have to use Mod function to express piecewise linear period functions.
In my case, two ...
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-2
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1
answer
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How Can I Visualize a PDE Boundary Condition? [closed]
I want to use Mathematica to visualize boundary/initial conditions for PDEs in 3-dimensional space. This was sparked by the initial comment in this question, which attempts to solve the PDE $$\...
- 129
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votes
2
answers
167
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What is the scope of the bug where Piecewise breaks DSolve?
Bug introduced after 9.0.1, persisting through 12.3.1. Fixed in 13.0
I have identified a bug in DSolve when differential equation includes a ...
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votes
1
answer
66
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Can't extend the function to continuous [closed]
I have code:
Am0[ω_] := Abs[H[I*ω]]
Am[ω_] := Piecewise[{{Limit[Am0[ω], ω -> 0], ω == 0}, {Am0[ω], ω!= 0}}]
Limit[Am0[ω], ω -> 0]
Am[0]
Function ...
4
votes
1
answer
159
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Sided Exclusions in Plot
Consider
Plot[Floor[x],{x,-5.5,5.5},ExclusionsStyle->{None,Blue}]
At each discontinuity, we get circles indicating the jump. Mathematically, ...
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3
votes
3
answers
88
views
Plotting the sign of a two-variables function
I have a continous function f(x,y), and I want the 2D plot of its sign. I then created a function
sign=Sign[f]
and used ...
- 33
4
votes
1
answer
341
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Problem with NDSolve and piecewise functions: Failure computing Filippov continuation
I am trying to solve a first order differential equation using NDSolve. The differential equation is
...
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2
votes
1
answer
399
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Discontinuity problem with 3D cylindrical heat equation (possibly due to a conversion between Cartesian to Cylindrical coordinates)
I have been working a certain type of 3D cylindrical diffusion equation for a bit now. I am trying to simulate a longitudinal diffusion process in a cylinder with a dislocation defect that will make ...
0
votes
2
answers
94
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Unpredictable behavior of a function
The Hermitian matrix mat is used to construct a function fun[x, y, z] as follows:
...
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votes
1
answer
315
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Ugly streaks caused by Arg in a contour plot
I had a more general question about a similar problem more than two years ago, Getting rid of discontinuities in plots caused by square roots, logarithms, `Arg`, etc, which got lots of interesting ...
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2
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366
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Approximate the piecewise constant with a smooth function
Let us first define a two regions as follow :
inner=1;outer=2;
reg1 = Disk[{0, 0}, inner];
reg2 = Annulus[{0, 0}, {inner, outer}];
glass=1.5;air=1;
Now let's say I ...
2
votes
2
answers
319
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Checking for discontinuities
There was an older post about checking the continuity of a function but the routines in the reply don't seem to work for my function. Hence the new post.
If I have a function
...
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votes
3
answers
404
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Boundary value problem with a DiracDelta
It seems that Mathematica can solve an initial value problem with a DiracDelta, but not a boundary value problem with a ...
- 6,607
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vote
1
answer
49
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sorting out the coordinate and respective solution values for plotting
I want to plot for coordinates and corresponding solution values below.
...
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votes
2
answers
145
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Benefits/downsides of defining function that is discontinuous at a point "explicitly" vs using piecewise?
For example, suppose I wanted to define a function, f that is $f(x)=x^2$ except at $x=1$, where $f(x)=5$
Two ways I can define this are
...
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2
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171
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Can someone please comment on the efficiency of Mathematica, Maple and Matlab in conditional plotting?
I use Mathematica to plot
...
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2
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Smooth Boxcar function (Rectangle Pulse function)
There are some answers on how to get a smooth squarewave function. But I would like to have a smooth boxcar function or rectangle function with 2 different widths.: ...
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3
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Solving a Nonlinear Complementary Problem (plasticity)
I would like to solve the following: given $t\mapsto\sigma(t)$ and $E>0$, $\sigma_y>0$, find $\epsilon$ such that:
$$\left\lbrace\begin{array}{l}g(t,\epsilon)\geq 0,\\ \phi(t,\epsilon,\epsilon')\...
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5
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3D FEM Vector Potential
I am trying to reproduce an FEM result in a paper. Due to possible copyright I cannot show the result directly but fortunately there is a free link
An Incomplete Gauge for 3D Nodal Finite Element ...
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2
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119
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Problem for defining continuously Eigenvectors from Kane and Mele model
The model is a simple eigenvalue problem. A matrix that depends on some parameters kx, ky, t, defined by:
...
1
vote
1
answer
171
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Continuity and derivability of a multivariable function at a specific point
I have this function:
f = Sqrt(Abs(x^2 - x*y))
So, how can I prove that it is derivable and/or continue in a point, like (0,0)?
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Inconsistent behavior of Limit function when evaluating a directed limit at a discontinuity
Consider the following expression:
(* In *) expr1 = Hold[Limit[Sign[x], x -> y, Direction -> "FromAbove"] == Sign[y]]
Now let's substitute a ...
- 777
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0
answers
52
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Is there a functionality to analytically find discontinutites of function?
I would like know whether it is somehow possible to analytically get discontinuities of a given function on a given interval (possibly with some reasonable assumption of the function otherwise being ...
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Exiting CrossSlidingDiscontinuity in NDSolve to follow equilibrium curve
I am trying to figure out how to get the solution curve to an NDSolve to slide along once it reaches a boundary and then to exit the ...
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Why does HeavisideTheta not have an implicit piecewise expansion?
The Heaviside step function implicitly expands to a piecewise function:
UnitStep[t - 3] // PiecewiseExpand
$$ \begin{cases} 1 & t\geq 3 \\ 0 & \text{...
- 301
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1
answer
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Computing limits from the left and right and getting the same answer which isn't correct
When I use the following code:
...
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655
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Mathematica is unable to compute the derivative of the function $\frac{\sin^2(x)}x$
Consider the function
$$f: \mathbb R\to\mathbb R, x\mapsto\begin{cases}\frac{\sin^2(x)}x, & x\neq 0, \\ 0, & x=0.\end{cases}$$
It is true that $f\in\mathcal C^1(\mathbb R)$ and that
$$f'(x)=\...
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0
answers
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Coupled nonlinear differential system with discontinuous functions which values are given by list elements, boundary conditions, NDSolve
I am very new to mathematica, I have googled my problem in vain, hope you can help me.
I am currently trying to solve a non linear system of two coupled differential equations given by (41) and (42). ...
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4
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How to model diffusion through a membrane?
This is a follow-up on How to handle discontinuity in diffusion coefficient?
Consider diffusion of $u(t,x)$ on the domain $x \in [0,2]$ with some simple boundary conditions such as $u(0) = 2, u(2) = ...
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How to handle discontinuity in diffusion coefficient?
I am looking to solve the diffusion equation with a discontinuous jump in the diffusion coefficient. In 1D, the diffusion equation for $u(t,x)$ is:
$$
\partial_t u = \partial_x (D \partial_x u),
$$
...
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2
answers
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IVP Piecewise ODE: Changing the Domain outside region of interest changes result dramatically
Good afternoon,
I am attempting to solve the following ODE:
...
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