Questions tagged [discontinuity]
Tag for issues caused by discontinuity (e.g. Boole, Piecewise, UnitStep, If, etc) in arithmetic function.
96
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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
...
- 22k
1
vote
2
answers
112
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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 ...
- 11
0
votes
1
answer
47
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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 ...
- 1
3
votes
1
answer
87
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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,
$$
g(x)= \begin{...
- 33
5
votes
1
answer
69
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NDEigensystem: 1D problem with discontinuous coefficients
I am trying to use NDEigensystem to solve the 1D problem
-cs[x]^2 vx''[x] = w^2 vx[x]
with vx[x] and w the eigenfunction and eigenvalue. The coefficient cs[x] is discontinuous at x = -xp, +xp and vx[x]...
- 85
4
votes
4
answers
188
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Parts of a Piecewise Matrix Function in NDSolve
First time posting.
Reproducing the Problem
I'm relatively new to Mathematica (using v.12.3), and working on a project. My problem can be reproduced with this.
...
- 113
1
vote
0
answers
71
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Numerical solution for multi-step PDEs
I am trying to numerically solve the following PDEs in MMA (v12.0)
$$\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(...
- 193
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votes
0
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Why does NDSolveValue give such different answers depending on the "Method" used and without indicating an error? [duplicate]
The first two inputs below only differ in the "Method" used in NDSolveValue for the solution of the heat equation in a composite yet they give no error (the error about BCs and ICs is ...
4
votes
3
answers
460
views
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 ...
- 139
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3
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488
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3
votes
1
answer
104
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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 ...
- 989
-2
votes
1
answer
146
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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
4
votes
2
answers
153
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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 ...
- 31.2k
0
votes
1
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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
130
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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, ...
- 3,099
3
votes
3
answers
84
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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
227
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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
285
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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:
...
- 339
8
votes
1
answer
294
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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 ...
- 2,092
3
votes
2
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274
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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
212
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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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4
votes
3
answers
342
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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 ...
- 6,214
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1
answer
47
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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
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136
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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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votes
2
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158
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Can someone please comment on the efficiency of Mathematica, Maple and Matlab in conditional plotting?
I use Mathematica to plot
...
- 1,089
5
votes
2
answers
928
views
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.: ...
- 1,701
8
votes
3
answers
238
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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')\...
- 13.9k
12
votes
4
answers
1k
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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 ...
- 191
0
votes
2
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97
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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
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1
answer
143
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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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2
votes
1
answer
73
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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 ...
- 757
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votes
0
answers
48
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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 ...
- 757
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votes
0
answers
49
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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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2
votes
1
answer
75
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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
$$ \begin{cases} 1 & t\geq 3 \\ 0 & \text{...
- 191
1
vote
1
answer
103
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Computing limits from the left and right and getting the same answer which isn't correct
When I use the following code:
...
- 1,765
8
votes
1
answer
488
views
Mathematica is unable to compute the derivative of the function $\frac{\sin^2(x)}x$
Consider the function
$$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)=\...
0
votes
0
answers
58
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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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votes
4
answers
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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) = ...
- 228k
9
votes
1
answer
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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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3
votes
2
answers
90
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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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1
answer
36
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1
vote
2
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91
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Plotting only one piece of an implicit 3d surface (the one value of the order parameter wich minimizes some free energy function)
I would like to plot a graphic of spontaneous magnetization vs T vs h for a Curie Weiss Model. The equation for stationary ...
- 13
6
votes
1
answer
481
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Strange result for sum $\sum _{k=1}^{\infty } \frac{\sin (k (k-1))}{k}$
In this sum over $k$
Sum[Sin[k (k - 1)]/k, {k, 1, ∞}]
the result still containes the summation index $k$.
...
- 12.8k
2
votes
1
answer
737
views
Repeated convergence test failure and why?
i have assigned all the values and the ODE assigned is as this
...
- 585
1
vote
1
answer
122
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Strange results from NDSolve after using a smooth (Tanh) function to approximate a discontinuous (jump) event
I am solving a system of ODE which contains a discontinuous ode (the equation v[t]== ...in the following code and it means that my ...
- 989
3
votes
3
answers
110
views
Dots at points of discontinuity
So, I got this code:
Plot[Piecewise[{{3, x <= 0}, {x^2 + 1, x > 0}}], {x, -2, 2},
PlotStyle -> {Purple}, Axes -> False, Frame -> True]
and I ...
- 33
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0
answers
416
views
How can I get continous plot of ArcTan over all quadrants?
Scope:
My calculation is an element in the optimization of a mechanism. The geometry is given by following equations. To get angles β and γ without using the inverse function ...
4
votes
3
answers
801
views
A discontinuity in an integral
I have a function which I'm trying to integrate, which is perfectly smooth and Mathematica sees it as well defined everywhere in the region over which I'm integrating it. The function is:
...
- 2,965
5
votes
1
answer
177
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Problem with using NDSolve on wave PDE on string
I am trying to verify my hand solution for wave PDE in 1D, on a string. The solution I get from NDSolve does not match the analytical solution.
This is a string, ...
- 116k