Questions tagged [discontinuity]

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

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34
votes
3answers
5k 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 ...
11
votes
3answers
801 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: <...
12
votes
3answers
3k 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 ...
7
votes
1answer
796 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: ...
16
votes
4answers
866 views

How to model diffusion through a membrane?

This is a follow-up on How to handle discontinuity in diffusion coefficient? Consider diffusion of $u(t,x)$ on the domain $x \in [0,2]$ with some simple boundary conditions such as $u(0) = 2, u(2) = ...
13
votes
1answer
2k 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 ...
12
votes
4answers
897 views

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 ...
6
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 ...
12
votes
3answers
1k 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 ...
5
votes
1answer
219 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
1answer
358 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 $$y=x$$, ...
4
votes
2answers
522 views

Smooth Boxcar function (Rectangle Pulse function)

There are some answers on how to get a smooth squarewave function. But I would like to have a smooth boxcar function or rectangle function with 2 different widths.: ...
7
votes
2answers
352 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: ...
2
votes
1answer
221 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: ...
10
votes
1answer
522 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: <...
6
votes
2answers
272 views

Ndsolve problem with Sign (friction)

In a very simple model I consider the motion of a body with frictional force. ...
5
votes
1answer
286 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 ...
1
vote
1answer
104 views

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 ...
9
votes
1answer
393 views

How to handle discontinuity in diffusion coefficient?

I am looking to solve the diffusion equation with a discontinuous jump in the diffusion coefficient. In 1D, the diffusion equation for $u(t,x)$ is: $$ \partial_t u = \partial_x (D \partial_x u), $$ ...
6
votes
2answers
686 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
94 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
0answers
72 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 ...
2
votes
1answer
110 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 ...
1
vote
1answer
541 views

Repeated convergence test failure and why?

i have assigned all the values and the ODE assigned is as this ...
-2
votes
1answer
121 views

How Can I Visualize a PDE Boundary Condition? [closed]

I want to use Mathematica to visualize boundary/initial conditions for PDEs in 3-dimensional space. This was sparked by the initial comment in this question, which attempts to solve the PDE $$\...