# Questions tagged [discontinuity]

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

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### Plotting only one piece of an implicit 3d surface (the one value of the order parameter wich minimizes some free energy function)

I would like to plot a graphic of spontaneous magnetization vs T vs h for a Curie Weiss Model. The equation for stationary ...
1k 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 ...
188 views

### Strange result for sum $\sum _{k=1}^{\infty } \frac{\sin (k (k-1))}{k}$

In this sum over $k$ Sum[Sin[k (k - 1)]/k, {k, 1, ∞}] the result still containes the summation index $k$. ...
674 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: ...
89 views

### 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 ...
58 views

### 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 ...
62 views

### 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 ...
246 views

### 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: ...
115 views

### Problem with using NDSolve on wave PDE on string

I am trying to verify my hand solution for wave PDE in 1D, on a string. The solution I get from NDSolve does not match the analytical solution. This is a string, ...
71 views

### Piecewise function not evaluating in NDSolve

Perhaps it's something obvious, but why does this simple piecewise function (as well as other conditionals) not evaluate in NDSolve: ...
182 views

### Ndsolve problem with Sign (friction)

In a very simple model I consider the motion of a body with frictional force. ...
607 views

### How to set interface conditions for optical waveguide in NDEigensystem?

I have been working on waveguide mode analysis using FEM in Mathematica for a week, but I haven't succeeded until now. The optical fiber-like waveguide is featured with different refractive index in ...
82 views

### NDSolve gives unexpected results when using the method of lines

I've been trying to solve the following PDE using the NDSolve function but it seems something is not working properly. The PDE is a the heat equation on polar coordinates and assuming angular simmetry:...
35 views

### Discontinuities in taking the roots of a complex function

I have the following functions e1, e2, and e3 which consists of the functions ...
145 views

### NDSolve with piecewise boundary conditions

I am trying to solve two simultaneous partial differential equation for $P[x,t]$ and $V[x,t]$. I have a piecewise boundary condition for $V[L,t]$. When using that piecewise condition, I get the error ...
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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: ...
180 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 ...
159 views

### NFourierTransform gives wrong result

This is my code: ...
4k 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 ...
258 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: <...
316 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} }]; ...
702 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: <...
590 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 ...
113 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 ...
2k 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 ...
183 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: ...
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 ...
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### 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 ...