Questions tagged [discontinuity]

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

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32
votes
3answers
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 ...
10
votes
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 ...
10
votes
3answers
673 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: <...
7
votes
1answer
599 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: ...
5
votes
4answers
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 ...
11
votes
1answer
1k 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 ...
5
votes
1answer
207 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: ...
7
votes
2answers
283 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: ...
6
votes
1answer
278 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 $$y=x$$, ...
7
votes
3answers
553 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 ...
6
votes
2answers
170 views

Ndsolve problem with Sign (friction)

In a very simple model I consider the motion of a body with frictional force. ...
5
votes
1answer
115 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 ...
6
votes
2answers
554 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 ...
5
votes
0answers
61 views

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 ...
2
votes
1answer
64 views

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 ...
2
votes
1answer
169 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: ...
2
votes
0answers
51 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 ...