# Questions tagged [discontinuity]

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

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### 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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### 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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### 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 ...
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### 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 ...
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### ContourPlot showing breaks in contours

I'm trying find graphically the solutions of the intersection of the following functions. ...
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### 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 ...
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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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### 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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### 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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### 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 ...
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### 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 ...
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### 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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### Problem in sharpness of Heaviside Function

The Heaviside function is not sharp, Do not know why? ...
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### 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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### 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 ...
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### 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: ...
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### 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 ...
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### NFourierTransform gives wrong result

This is my code: ...
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### 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: <...
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### 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} }]; ...
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### 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 ...