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Questions tagged [discontinuity]

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

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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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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, ...
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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
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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 ...
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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
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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
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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
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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
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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
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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 ...
4
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2answers
210 views

Problem in sharpness of Heaviside Function

The Heaviside function is not sharp, Do not know why? ...
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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?
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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
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1answer
146 views
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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
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2answers
126 views
4
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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
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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
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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
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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
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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
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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
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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: ...
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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
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3answers
282 views

How to complete function which is not defined for all interval

I have a function testF22 like this ...
5
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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
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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 ...
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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
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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
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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
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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
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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 ...