Questions tagged [discontinuity]
Tag for issues caused by discontinuity (e.g. Boole, Piecewise, UnitStep, If, etc) in arithmetic function.
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1answer
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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.
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0
votes
2answers
41 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, ...
0
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0answers
41 views
How to get rid of the discontinuities in the plots and animation?
Trying to plot the angles for a double pendulum against each other such that they stay within the bounds of -Pi to Pi. The NDSolve solves the equations such that if a pendulum does a full loop the ...
6
votes
2answers
82 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 ...
1
vote
2answers
73 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
...
3
votes
2answers
80 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:
$$ x'...
3
votes
1answer
73 views
WhenEvent - energy conservation not valid [closed]
I would like to simulate the following conservative system, with purely elastic impacts (coefficient of restitution is 1). Applying the WhenEvents the energy of the system is not conserved.
How can I ...
6
votes
1answer
245 views
The rectangular region composed of two triangular regions contains a pde connecting the bc of the first and the second kind
I'm going to solve the Laplacian equation of the electrostatic field, which consists of two triangular regions, a rectangular region, a square, and on the intersection of the two regions of $$y=x$$, ...
2
votes
1answer
32 views
Summations with power of DiscreteDelta
Expression
Sum[DiscreteDelta[a - 1]^2, {a, -∞, ∞}]
evaluates to 1, as expected, but
Sum[DiscreteDelta[a - b]^2, {a, -∞, ∞}]
does not converge, according to ...
2
votes
0answers
39 views
How to express continuity assumption for Integrate?
I am wondering if it is possible, and how if so, to express function continuity in the assumptions for the definite form of Integrate.
First of all, while
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4
votes
2answers
210 views
Problem in sharpness of Heaviside Function
The Heaviside function is not sharp, Do not know why?
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1
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0answers
52 views
Saturation function in Mathematica [duplicate]
In Simulink, there is a function called Saturation:
Is there function like that in Mathematica? If yes, what is it called?
0
votes
1answer
91 views
Piecewise continuation of a discrete function on an area
I have a discrete function (finite set of values) defined on an area $\Omega$ in $R^2$. Each value of the function is defined on a subarea $\Omega_i$(triangle in my case). These triangles account for ...
2
votes
1answer
146 views
NDSolve cannot do a discontinuity replacement for event surfaces that depend only on time
I'm trying to solve a system of DAEs with discrete conditions:
...
0
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0answers
127 views
NDSolve unable to handle discontinuities
I'm trying to solve a set of ordinary non-linear differential equations but running into issues. Specifically, after supplying Mathematica the below definitions and evaluating the ...
1
vote
2answers
126 views
4
votes
1answer
169 views
Options of WhenEvent
I'm using NDSolve and WhenEvent to simulate building heating systems and their discontinuous operation. Here is a simplified example.
The idea is quite simple. I have the following WhenEvents:
<...
2
votes
1answer
196 views
Force derivative of piecewise function at boundary points to be one-sided derivative
I've defined a smooth step function given as
f[x_] = Piecewise[{
{y0, x<x0-dx/2},
{y0+1/2(y1-y0)(1-Cos[Pi*x/dx]), x<x0+dx/2},
{y0, True}
}];
...
6
votes
2answers
459 views
Solving wave equation with singular initial conditions
I am trying to compute the solution to the wave equation using NDSolveValue and singular initial displacement (continuous, but not differentiable in a point). I ...
3
votes
0answers
81 views
NDSolve produces different solutions for the same set of equations [duplicate]
I've tried to simulate simple mechanical system - mass which is pulled on a spring. The code You can find below. Unfortunately, I can't get correct results. But, what has surprised me more, is that ...
1
vote
1answer
522 views
A discontinuity in a plot of a continuous function
I plot a continuous, though not a smooth function:
Plot[If[a >= 0.5, 0, Sqrt[0.5 - a]], {a, -1, 1}, PlotRange -> All]
which returns the following
One can ...
2
votes
1answer
144 views
Piecewise causes ndnum warning in NDSolve
Bug introduced in 8.0.4 or earlier.
I try to solve the heat transfer equation with boundary condition that depends on time:
...
7
votes
1answer
532 views
Free Convective Heat Transfer of Non-Newtonian Power Law Fluids from a Vertical Plate
I am trying to solve a set of PDEs mentioned in this paper with NDSolve but facing quite a few issues.
The PDE system is:
...
7
votes
2answers
252 views
NDSolve with Piecewise solving BVP gives warning bvdisc [duplicate]
Backslide introduced in 9.0, persisting through 11.0.1
I try to solve a boundary value problem of coupled ODEs. For reference, when I solve this set of equations it works without any problems:
...
8
votes
3answers
588 views
Position of discontinuous coefficient influences the solution of PDE
This issue is raised in the discussion under this post about heat flux continuity and I think it's better to start a new question to state it in a clearer way. Just consider the following example:
<...
5
votes
3answers
282 views
How to complete function which is not defined for all interval
I have a function testF22 like this
...
1
vote
2answers
173 views
5
votes
1answer
193 views
Discontinuous boundary condition distorts in the numeric solution
Here I want to simulate a physical model that I have used a set of differential equations.
My coefficients and parameters:
...
11
votes
1answer
981 views
NDSolveValue - Heat flux continuity
I'm having some problems with NDSolve and the problem of conduction of heat. Specifically I'm having problems with the continuity of heat flux. First, let me ...
4
votes
2answers
364 views
Can't use my own discontinuous coefficient within NDSolve
I want to evaluate the pendulum's motion with changing equilibrium state given by eqilValue[t]:
...
7
votes
1answer
2k views
NDSolve and Piecewise functions [duplicate]
Backslide introduced in 9.0, persisting through 11.0.1
I want to clarify upfront, This is not a please help me get the answer to my homework question. I know what I need to do I just do not know how ...
9
votes
3answers
2k views
Can NDSolve handle discontinuous data?
Backslide introduced in 9.0, persisting through 11.0.1
It is possible to numerically solve a differential equation if not-smooth data are involved?
For example the following instruction return the ...
32
votes
3answers
3k views
Plot a piecewise function with black and white disks marking discontinuities
Let's say I'd like to plot Sign[x + 0.5]:
Plot[Sign[x + 0.5], {x, -1, 1}]
Mathematica will give this:
This plot does not ...
5
votes
4answers
1k views
NDSolve with Piecewise gives the incorrect answer randomly
Bug introduced in 9.0 and fixed in 11.1
NDSolve in Mathematica 9.0.0 (MacOS) is behaving strangely with a piecewise right hand side. The following code (a ...
