Questions tagged [discontinuity]
Tag for issues caused by discontinuity (e.g. Boole, Piecewise, UnitStep, If, etc) in arithmetic function.
77
questions
3
votes
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
votes
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
votes
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 ...
1
vote
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
votes
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
...
0
votes
2answers
139 views
Can someone please comment on the efficiency of Mathematica, Maple and Matlab in conditional plotting?
I use Mathematica to plot
...
3
votes
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
votes
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:
$$\left\lbrace\begin{array}{l}g(t,\epsilon)\geq 0,\\ \phi(t,\epsilon,\epsilon')\...
12
votes
4answers
602 views
3D FEM Vector Potential
I am trying to reproduce an FEM result in a paper. Due to possible copyright I cannot show the result directly but fortunately there is a free link
An Incomplete Gauge for 3D Nodal Finite Element ...
0
votes
2answers
45 views
Problem for defining continously Eigenvectors from Kane and Mele model
The model is a simple eigenvalue problem. A matrix that depends on some parameters kx, ky, t, defined by:
...
1
vote
1answer
78 views
Continuity and derivability of a multivariable function at a specific point
I have this function:
f = Sqrt(Abs(x^2 - x*y))
So, how can I prove that it is derivable and/or continue in a point, like (0,0)?
2
votes
1answer
50 views
Inconsistent behavior of Limit function when evaluating a directed limit at a discontinuity
Consider the following expression:
(* In *) expr1 = Hold[Limit[Sign[x], x -> y, Direction -> "FromAbove"] == Sign[y]]
Now let's substitute a ...
0
votes
0answers
45 views
Is there a functionality to analytically find discontinutites of function?
I would like know whether it is somehow possible to analytically get discontinuities of a given function on a given interval (possibly with some reasonable assumption of the function otherwise being ...
0
votes
0answers
41 views
Exiting CrossSlidingDiscontinuity in NDSolve to follow equilibrium curve
I am trying to figure out how to get the solution curve to an NDSolve to slide along once it reaches a boundary and then to exit the ...
2
votes
1answer
49 views
Why does HeavisideTheta not have an implicit piecewise expansion?
The Heaviside step function implicitly expands to a piecewise function:
UnitStep[t - 3] // PiecewiseExpand
$$ \begin{cases} 1 & t\geq 3 \\ 0 & \text{...
1
vote
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
votes
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
$$f'(x)...
0
votes
0answers
53 views
Coupled nonlinear differential system with discontinuous functions which values are given by list elements, boundary conditions, NDSolve
I am very new to mathematica, I have googled my problem in vain, hope you can help me.
I am currently trying to solve a non linear system of two coupled differential equations given by (41) and (42). ...
16
votes
4answers
655 views
How to model diffusion through a membrane?
This is a follow-up on How to handle discontinuity in diffusion coefficient?
Consider diffusion of $u(t,x)$ on the domain $x \in [0,2]$ with some simple boundary conditions such as $u(0) = 2, u(2) = ...
8
votes
1answer
246 views
How to handle discontinuity in diffusion coefficient?
I am looking to solve the diffusion equation with a discontinuous jump in the diffusion coefficient. In 1D, the diffusion equation for $u(t,x)$ is:
$$
\partial_t u = \partial_x (D \partial_x u),
$$
...
3
votes
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:
...
0
votes
0answers
35 views
1
vote
1answer
34 views
1
vote
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
votes
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, ā}]
the result still containes the summation index $k$.
...
1
vote
1answer
252 views
Repeated convergence test failure and why?
i have assigned all the values and the ODE assigned is as this
...
1
vote
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
votes
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
votes
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 ...
0
votes
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 Ī² and Ī³ without using the inverse function ...
4
votes
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
votes
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
votes
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
votes
2answers
240 views
Ndsolve problem with Sign (friction)
In a very simple model I consider the motion of a body with frictional force.
...
12
votes
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
votes
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:...
1
vote
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
votes
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
votes
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
votes
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
votes
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
votes
1answer
66 views
ContourPlot showing breaks in contours
I'm trying find graphically the solutions of the intersection of the following functions.
...
0
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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 $$y=x$$, ...
