Questions tagged [discontinuity]

Tag for issues caused by discontinuity (e.g. Boole, Piecewise, UnitStep, If, etc) in arithmetic function.

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3
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2answers
129 views

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
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2answers
104 views

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 ...
4
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3answers
302 views

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 ...
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1answer
38 views

sorting out the coordinate and respective solution values for plotting

I want to plot for coordinates and corresponding solution values below. ...
2
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2answers
101 views

Benefits/pitfalls 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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2answers
139 views
3
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2answers
273 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.: ...
5
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3answers
183 views

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')\...
12
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4answers
602 views

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 ...
0
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2answers
45 views

Problem for defining continously 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: ...
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1answer
78 views

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)?
2
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1answer
50 views

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 ...
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0answers
45 views

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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0answers
41 views

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 ...
2
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1answer
49 views

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{...
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1answer
65 views

Computing limits from the left and right and getting the same answer which isn't correct

When I use the following code: ...
8
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1answer
257 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 clear that $f\in\mathcal C^1(\mathbb R)$ and that $$f'(x)...
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0answers
53 views

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). ...
16
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4answers
655 views

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) = ...
8
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1answer
246 views

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: $$ \partial_t u = \partial_x (D \partial_x u), $$ ...
3
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2answers
82 views

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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0answers
35 views

Problem when integrating a discontinuous function

I have this simple code: ...
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1answer
34 views

Problem with Exclusions when Floor is used

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2answers
79 views

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 ...
6
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1answer
312 views

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 $k$. ...
1
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1answer
252 views

Repeated convergence test failure and why?

i have assigned all the values and the ODE assigned is as this ...
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1answer
90 views

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 ...
4
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3answers
279 views

NDSolve will try solving the system as differential-algebraic equations but it didn't get the solution

Please help me deal with this kind of question about ODEs. My codes are as follows ...
3
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3answers
70 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 ...
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0answers
180 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
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3answers
544 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: ...
5
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1answer
141 views

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, ...
3
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1answer
81 views

Piecewise function not evaluating in NDSolve

Perhaps it's something obvious, but why does this simple piecewise function (as well as other conditionals) not evaluate in NDSolve: ...
6
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2answers
240 views

Ndsolve problem with Sign (friction)

In a very simple model I consider the motion of a body with frictional force. ...
12
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3answers
920 views

How to set interface conditions for optical waveguide in NDEigensystem?

I have been working on waveguide mode analysis using FEM in Mathematica for a week, but I haven't succeeded until now. The optical fiber-like waveguide is featured with different refractive index in ...
0
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1answer
87 views

NDSolve gives unexpected results when using the method of lines

I've been trying to solve the following PDE using the NDSolve function but it seems something is not working properly. The PDE is a the heat equation on polar coordinates and assuming angular simmetry:...
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0answers
60 views

Discontinuities in taking the roots of a complex function

I have the following functions e1, e2, and e3 which consists of the functions ...
5
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1answer
210 views

NDSolve with piecewise boundary conditions

I am trying to solve two simultaneous partial differential equation for $P[x,t]$ and $V[x,t]$. I have a piecewise boundary condition for $V[L,t]$. When using that piecewise condition, I get the error ...
5
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2answers
330 views

Heat equation with variable conductivity

Let us consider the (very simple) problem $\qquad \partial_x[k(x)\,\partial_xu]=0,\quad x\in [0,1]$ $\qquad u(0)=0,\ u(1)=1,$ with $l\in(0,1)$ $\qquad k(x)=\left\{\begin{array}{l}k_1^{},x<l\\k_2^...
5
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0answers
87 views

Evaluation of Mod of InterpolatingFunction prevents discontinuity processing by Plot

While trying out @MichaelSeifert's answer to Eliminating Discontinuities When Using Mod with NDSolve and Plot for Oscillators, I came across this odd behavior. Depending on how an ...
2
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1answer
94 views

Eliminating Discontinuities When Using Mod with NDSolve and Plot for Oscillators

I have found similar questions to mine, but dealing with piecewise and parametric plots instead and unfortunately the answers don't seem to extend to my case. I have a solution from ...
0
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1answer
66 views

ContourPlot showing breaks in contours

I'm trying find graphically the solutions of the intersection of the following functions. ...
0
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1answer
264 views

Finding the discontinuities of a function

I have a list of data and I want to find the discontinuities in the plot of them but I don't want to use interpolation because it is not that exact that it should be. is there any other way? The ...
0
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1answer
64 views

Defining a function with a point of finite discontinuity [closed]

I wrote the code for the function $T$ defined on $[0,1]$ by $T(x)=\frac{x+2}{3}$ if $x\neq\frac{1}{2}$ and $T(\frac{1}{2})=1$ as follows. ...
0
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2answers
126 views

How to plot 3D discontinuous iterative plot?

I am having troubles with plotting this set of data triples={{0, 1, 1}, {9/50, 4/5, 1}}, {{9/50, 4/5, 1}, {3/8, 4/5, 1}}, {{3/8, 58333/100000, 1}, {3/4, 16667/100000, 1}}, {{3/4, 0, 1}, {1, 0, ...
6
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2answers
209 views

Finding a removable singularity

I have more complex functions than this, but say I just have: f[x_]:=(x-a)/(x-2) The function is not defined for x==2. I ...
2
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2answers
270 views

Solving an ODE with a sign/step function which depends on the time derivative

I'm trying to solve a set of ODEs with a Heaviside step function which depends on the sign of the derivative of the function. This is a simplifying example of what I'm trying to do ...
5
votes
2answers
183 views

Using NDSolve with conditional expression

I am trying to solve the 2nd order ODE for a harmonic oscillator under the influence of a harmonic restoring force, a sliding friction force, and a static friction force. My equations are below: $$ x'...
3
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1answer
95 views

WhenEvent - energy conservation not valid [closed]

I would like to simulate the following conservative system, with purely elastic impacts (coefficient of restitution is 1). Applying the WhenEvents the energy of the system is not conserved. How can I ...
7
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1answer
341 views

The rectangular region composed of two triangular regions contains a pde connecting the bc of the first and the second kind

I'm going to solve the Laplacian equation of the electrostatic field, which consists of two triangular regions, a rectangular region, a square, and on the intersection of the two regions of $$y=x$$, ...