# Questions tagged [discontinuity]

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

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### Issue with a Piecewise Diffusion Problem [duplicate]

I'm working on a piecewise diffusion problem in Mathematica where the diffusion coefficient is 1 in the first region (x ≤ 1) and 2 in the second region (x > 1). The initial condition is also ...
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### NDSolve::nlnum and NDSolve::bcedge

I'm trying to address a mass diffusion problem, and I'm encountering two problems. ...
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### Possible bug in partial derivative [closed]

In 14.0 on Windows 10 let us consider D[Min[x, y], x] Piecewise[{{1, x - y <= 0}}, 0] As I understand it, the result is ...
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### Scaling DiracComb does not work properly in NDSolve

The code below is for a simple first order ADC converter and works properly. DiracComb is to sample the signal y[t]. ...
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### Tell Mathematica that the output of a function is a List / Vector

I have a function (Piecewise) that returns a list, e.g.: F[x_] := Piecewise[{{{x^2, x}, x < 0}, {{x, x^2}, x > 0}}, {0, 0}]; I would like to add another list ...
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### How to remove artefacts in Plot3D?

Consider the following code Plot3D[ArcTan[x/y] + ArcTan[y/x], {x, -1, 1}, {y, -1, 1}] Is it possible to remove the "dragging" artefacts observed at the ...
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### How to make the segmentation function automatically draw the correct function image at the break point?

The function is: We know that f[x] is an even function defined on x < 0 And x > 0, when x > 0, ...
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### Machine overflow when defining boundary conditions

Recently I have been trying to code Maxwell's equations over a closed surface and have been facing some trouble defining the boundary conditions for the magnetic field. The equation for the normal of ...
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### Numerical solution of a nonlinear PDE that develops a growing piecewise linear region

I am trying to improve the numerical solution of some PDEs that develop a piecewise behavior during their evolution. The simplest example of one such PDE is for a function $u(t,x)$ with $t \in [-T,T]$ ...
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### VectorPlot "Part 1 of {} does not exist" error

Bug introduced in 7.0, persisting through 13.2. I am looking to plot the Magnetic Vector potential, A, as a function of position along the edge of a density plot. The density plot is fine, and I ...
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### Why does contour plot not show point(s) where function has a discontinuity?

Consider the following code, which defines a function with a discontinuity, and then generates a contour plot when the function equals that discontinuity. ...
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### Solve computes discontinuous eigenvalues of parameter-dependent matrix

So I have a family of unitary matrices $m(x,y)$, which depend on two parameters $x,y \in [0, 2 \pi)$. Its eigenvalues should be continuous in $(x,y)$. Since $m(x,y)$ is a unitary matrix, its ...
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### Piecewise Boundary Condition for axisymmetric heat equation [duplicate]

I'm trying to solve the 2D axisymmetric heat equation, where only one section of the tube is being heated up. I have written the following code below: ...
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### Discontinuous ODE results in NDSolve::ndinid warning, initial condition is not in the range specified by the discrete variable (internal variable)

The equations and code are below. The short version is: I know the error is because NDSolve is doing something in the background to handle the discontinuous ODE. ...
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### 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 ...
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1 vote
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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
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### 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)?
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### 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 ...
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