Questions tagged [discontinuity]

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

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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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1 vote
0 answers
66 views

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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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 ...
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3 votes
3 answers
450 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 ...
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8 votes
3 answers
467 views

How to make all the balls move until they stop by NBodySimulation

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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 votes
1 answer
135 views

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 $$\...
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4 votes
2 answers
148 views

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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1 answer
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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 ...
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4 votes
1 answer
115 views

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
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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 ...
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4 votes
1 answer
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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
260 views

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 ...
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0 votes
2 answers
94 views

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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8 votes
1 answer
287 views

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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3 votes
2 answers
221 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 ...
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2 votes
2 answers
183 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 ...
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4 votes
3 answers
339 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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1 vote
1 answer
47 views

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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2 votes
2 answers
106 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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2 answers
157 views

Can someone please comment on the efficiency of Mathematica, Maple and Matlab in conditional plotting?

I use Mathematica to plot ...
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5 votes
2 answers
767 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.: ...
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8 votes
3 answers
221 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')\...
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12 votes
4 answers
1k 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 ...
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0 votes
2 answers
90 views

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: ...
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1 vote
1 answer
133 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)?
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2 votes
1 answer
71 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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0 answers
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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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0 votes
0 answers
48 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 ...
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2 votes
1 answer
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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{...
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1 vote
1 answer
98 views

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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8 votes
1 answer
463 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)=\...
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0 votes
0 answers
58 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). ...
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16 votes
4 answers
961 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) = ...
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9 votes
1 answer
462 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: $$ \partial_t u = \partial_x (D \partial_x u), $$ ...
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3 votes
2 answers
88 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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1 vote
1 answer
35 views

Problem with Exclusions when Floor is used

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1 vote
2 answers
90 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 ...
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6 votes
1 answer
465 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 $k$. ...
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1 vote
1 answer
655 views

Repeated convergence test failure and why?

i have assigned all the values and the ODE assigned is as this ...
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1 vote
1 answer
111 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 ...
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3 votes
3 answers
102 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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0 votes
0 answers
388 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 ...
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4 votes
3 answers
780 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: ...
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5 votes
1 answer
167 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, ...
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  • 108k
3 votes
1 answer
130 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: ...
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6 votes
2 answers
288 views

Ndsolve problem with Sign (friction)

In a very simple model I consider the motion of a body with frictional force. ...
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12 votes
3 answers
1k 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 ...
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  • 4,685
0 votes
1 answer
103 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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1 vote
0 answers
78 views

Discontinuities in taking the roots of a complex function

I have the following functions e1, e2, and e3 which consists of the functions ...
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