# Questions tagged [discontinuity]

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

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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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### Why does NDSolveValue give such different answers depending on the "Method" used and without indicating an error? [duplicate]

The first two inputs below only differ in the "Method" used in NDSolveValue for the solution of the heat equation in a composite yet they give no error (the error about BCs and ICs is ...
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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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### 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 ...
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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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### Repeated convergence test failure and why?

i have assigned all the values and the ODE assigned is as this ...
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### 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 ...
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### 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 ...
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### 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 β and γ without using the inverse function ...
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### 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: ...
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