Questions tagged [discontinuity]

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

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1
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1answer
26 views

Problem with Exclusions when Floor is used

...
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2answers
66 views

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 ...
6
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1answer
195 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 $k$. ...
1
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1answer
94 views

Repeated convergence test failure and why?

i have assigned all the values and the ODE assigned is as this ...
1
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1answer
76 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 ...
4
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3answers
203 views

NDSolve will try solving the system as differential-algebraic equations but it didn't get the solution

Please help me deal with this kind of question about ODEs. My codes are as follows ...
3
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3answers
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 ...
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0answers
67 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 ...
4
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3answers
281 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: ...
5
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1answer
117 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, ...
3
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1answer
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: ...
6
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2answers
185 views

Ndsolve problem with Sign (friction)

In a very simple model I consider the motion of a body with frictional force. ...
9
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3answers
627 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 ...
0
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1answer
83 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:...
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0answers
36 views

Discontinuities in taking the roots of a complex function

I have the following functions e1, e2, and e3 which consists of the functions ...
5
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1answer
148 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 ...
5
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2answers
246 views

Heat equation with variable conductivity

Let us consider the (very simple) problem $\qquad \partial_x[k(x)\,\partial_xu]=0,\quad x\in [0,1]$ $\qquad u(0)=0,\ u(1)=1,$ with $l\in(0,1)$ $\qquad k(x)=\left\{\begin{array}{l}k_1^{},x<l\\k_2^...
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0answers
73 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 ...
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1answer
71 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 ...
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1answer
64 views

ContourPlot showing breaks in contours

I'm trying find graphically the solutions of the intersection of the following functions. ...
0
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1answer
141 views

Finding the discontinuities of a function

I have a list of data and I want to find the discontinuities in the plot of them but I don't want to use interpolation because it is not that exact that it should be. is there any other way? The ...
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1answer
62 views

Defining a function with a point of finite discontinuity [closed]

I wrote the code for the function $T$ defined on $[0,1]$ by $T(x)=\frac{x+2}{3}$ if $x\neq\frac{1}{2}$ and $T(\frac{1}{2})=1$ as follows. ...
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2answers
102 views

How to plot 3D discontinuous iterative plot?

I am having troubles with plotting this set of data triples={{0, 1, 1}, {9/50, 4/5, 1}}, {{9/50, 4/5, 1}, {3/8, 4/5, 1}}, {{3/8, 58333/100000, 1}, {3/4, 16667/100000, 1}}, {{3/4, 0, 1}, {1, 0, ...
6
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2answers
164 views

Finding a removable singularity

I have more complex functions than this, but say I just have: f[x_]:=(x-a)/(x-2) The function is not defined for x==2. I ...
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2answers
126 views

Solving an ODE with a sign/step function which depends on the time derivative

I'm trying to solve a set of ODEs with a Heaviside step function which depends on the sign of the derivative of the function. This is a simplifying example of what I'm trying to do ...
5
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2answers
127 views

Using NDSolve with conditional expression

I am trying to solve the 2nd order ODE for a harmonic oscillator under the influence of a harmonic restoring force, a sliding friction force, and a static friction force. My equations are below: $$ x'...
3
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1answer
89 views

WhenEvent - energy conservation not valid [closed]

I would like to simulate the following conservative system, with purely elastic impacts (coefficient of restitution is 1). Applying the WhenEvents the energy of the system is not conserved. How can I ...
6
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1answer
293 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 $$y=x$$, ...
2
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1answer
35 views

Summations with power of DiscreteDelta

Expression Sum[DiscreteDelta[a - 1]^2, {a, -∞, ∞}] evaluates to 1, as expected, but Sum[DiscreteDelta[a - b]^2, {a, -∞, ∞}] does not converge, according to ...
2
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0answers
54 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 ...
4
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2answers
312 views

Problem in sharpness of Heaviside Function

The Heaviside function is not sharp, Do not know why? ...
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0answers
83 views

Saturation function in Mathematica [duplicate]

In Simulink, there is a function called Saturation: Is there function like that in Mathematica? If yes, what is it called?
0
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1answer
156 views

Piecewise continuation of a discrete function on an area

I have a discrete function (finite set of values) defined on an area $\Omega$ in $R^2$. Each value of the function is defined on a subarea $\Omega_i$(triangle in my case). These triangles account for ...
2
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1answer
252 views

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: ...
1
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0answers
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 ...
1
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2answers
162 views

NFourierTransform gives wrong result

This is my code: ...
7
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1answer
294 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: <...
2
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1answer
329 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} }]; ...
6
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2answers
602 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 ...
3
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0answers
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 ...
2
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2answers
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 ...
2
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1answer
185 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: ...
7
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1answer
675 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: ...
7
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2answers
296 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: ...
11
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3answers
711 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: <...
5
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3answers
314 views

How to complete function which is not defined for all interval

I have a function testF22 like this ...
1
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2answers
202 views
5
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1answer
213 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: ...
12
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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 ...
4
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2answers
394 views

Can't use my own discontinuous coefficient within NDSolve

I want to evaluate the pendulum's motion with changing equilibrium state given by eqilValue[t]: ...