Questions tagged [discontinuity]

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

Filter by
Sorted by
Tagged with
4 votes
1 answer
90 views

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 views

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 views

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 views

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 views

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]...
4 votes
4 answers
188 views

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. ...
1 vote
0 answers
71 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(...
  • 193
0 votes
0 answers
54 views

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 ...
9 votes
3 answers
488 views

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

...
  • 24.6k
3 votes
1 answer
104 views

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 ...
-2 votes
1 answer
146 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 $$\...
  • 129
4 votes
2 answers
153 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 ...
  • 31.2k
0 votes
1 answer
62 views

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 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, ...
  • 3,099
3 votes
3 answers
84 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
227 views

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 ...
  • 145
2 votes
1 answer
285 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 ...
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: ...
  • 339
8 votes
1 answer
294 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 ...
3 votes
2 answers
274 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 votes
2 answers
212 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 votes
3 answers
342 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 ...
  • 6,214
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. ...
6 votes
2 answers
136 views

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 ...
0 votes
2 answers
158 views

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 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')\...
  • 13.9k
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 ...
  • 191
0 votes
2 answers
97 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: ...
1 vote
1 answer
143 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)?
  • 121
2 votes
1 answer
73 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 ...
0 votes
0 answers
48 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 ...
0 votes
0 answers
49 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 ...
  • 1
2 votes
1 answer
75 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{...
1 vote
1 answer
103 views

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 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). ...
  • 912
16 votes
4 answers
1k 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) = ...
  • 228k
9 votes
1 answer
527 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: $$ \partial_t u = \partial_x (D \partial_x u), $$ ...
  • 228k
3 votes
2 answers
90 views

IVP Piecewise ODE: Changing the Domain outside region of interest changes result dramatically

Good afternoon, I am attempting to solve the following ODE: ...
1 vote
1 answer
36 views

Problem with Exclusions when Floor is used

...
  • 1,397
1 vote
2 answers
91 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 votes
1 answer
481 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 $k$. ...
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 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 ...
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 ...
0 votes
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: ...
5 votes
1 answer
177 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, ...
  • 116k