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Questions tagged [singularity]

Questions involving expressions that assume infinite values within the computational range; often associated with NDSolve, NIntegrate, etc.

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108 views

RandomVariate with ProbabilityDistribution performs well in 10.0, but not in later versions

I have a custom probability distribution function and I want to generate numbers according to this PDF. Interestingly enough, this works without trouble on my MacBook with Mathematica 10.0, but when I ...
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1answer
78 views

Adding a limit in NDSolve to avoid division by zero

I'm trying to solve a set of differential equations in which one of the functions that describe the time derivative gets values which make it divide by zero ...
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1answer
96 views

Numerical integration giving trouble

I am trying to do the following integral numerically, $$\rho(\theta_{j},\phi_{j})=\int\frac{\sin{\theta_{i}} d\theta_{i} d\phi_{i}}{\sqrt{2+2[\cos(\theta_{i})\cos(\theta_{j})+\sin{\theta_{i}\sin{\...
2
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0answers
63 views

Solving 2d non-linear PDE with singular sources numerically [closed]

I would like to hear some suggestions on how to numerically solve a 4d Poisson equation with two singular sources, which can be brought to the following form (thanks to symmetries) \begin{equation} \...
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0answers
109 views

Stokes theorem in Mathematica

I came across this problem in calculus. It makes a handwavy sense with the explanation provided. I have tried to prove it in MMA: ...
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0answers
48 views

Unexpected breaks in a smooth plot

I have the following code leading to a broken plot. However, I physical intuition (based on the problem I am dealing with) says that there should be a continuous curve. ...
5
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0answers
149 views

StiffSystem or Singularity - a system of second order ODEs in the problem of geodesics

I would be extremely grateful for any help regarding the following code I wrote and the errors it produces. In this code I am investigating the behaviour of a massive particle trapped in the vicinity ...
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1answer
76 views

NDSolve for coupled differential equations with large coefficient

I have three coupled differential equations to solve. Those equations are ...
4
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1answer
68 views

Numerical continuation methods for bypassing a singularity when integrating an ODE

Here is the ODE I want to numerically integrate, odey=-l (1 + l) R[y] + (k - y) (-2 Derivative[1][R][y] + (k - y) (R^\[Prime]\[Prime])[y]) If we rearrange it in ...
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3answers
142 views

NDSolve fails at the regular singular point of a second-order ODE

Here is the ODE I want to numerically integrate, odey=-l (1 + l) R[y] + (k - y) (-2 Derivative[1][R][y] + (k - y) (R^\[Prime]\[Prime])[y]) If we rearrange it in ...
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1answer
75 views

NDSolve and interpolating function

What could possibly went wrong in my code? Basically, I am solving the differential equation $\textbf{ode}$ using $\textbf{NDSolve}$. But mathematica says, NDSolve::mxst: Maximum number of 10000 steps ...
3
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1answer
284 views

1st-order linear ODE system gives inaccurate/biased solutions

Consider an ODE eigensystem $$ t(y+\frac{1}{s})a(y)+[(q+\frac{1}{2}+\frac{s}{2}y)+s(y\partial_y+\frac{1}{2})]b(y)=\lambda a(y)\\ t(y+\frac{1}{s})b(y)+[(q+\frac{1}{2}+\frac{s}{2}y)-s(y\partial_y+\frac{...
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1answer
74 views

Singularities forming on boundary while solving system of pde's

This is a follow up of a previous question I asked regarding solving a system of coupled, non-linear partial differential equations, 2D spatially + time. The equations (shown below) model a magnetic ...
4
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2answers
80 views

Why do I get “PrincipalValue cannot work with the specified exclusions” when feeding a list to a function? [closed]

I have the following test function which I want to evaluate at various points from $x=0$ to $5$: $f(x) = \int^{20}_{1}\frac{1}{x-y} dy$ There's clearly a singularity here in the integral at $x=y$, ...
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0answers
36 views

NDSolve dealing with message infinite expression and non numerical value non homogeneous differential equation

I'm trying to solve the following differential equation with some specific conditions ...
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1answer
65 views
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2answers
94 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'...
2
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1answer
127 views

4D NIntegrate with singularities

I need to integrate a function in a 4D region (x1,y1,x2,y2), which explodes whenever x1=x2&&y1=y2. The code is as following: ...
2
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1answer
127 views

StreamPlot and VectorPlot handling of functions with singularities

Mathematica's Plot can handle plotting functions with singularities From http://reference.wolfram.com/language/tutorial/BasicPlotting.html You can plot ...
2
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1answer
135 views

NIntegrate: NumericQ and derivatives

I need to integrate a function with a singularity at the origin. I need this integration to happen quite fast, and while Integrate[] simply keeps on going forever, using NIntegrate with LocalAdaptive ...
0
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1answer
82 views

Numerically integrate function with sudden jumps

I want to integrate the function Log [ (x^2 + t^2 + m^2 + 50^2)/( x^2 + t^2 + m^2)] Exp[-((x + y)^2/(2 0.00001))] for x,t and y between -50 and 50. This ...
5
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0answers
139 views

Using NDSolve on the Painlevé equations

In an earlier question of mine, I was looking for a way to handle certain kinds of singularities (poles) when using NDSolve. Michael E2's answer, which relied on projective geometry was the most ...
10
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2answers
416 views

Fredholm Integral Equation of the 2nd Kind with a Singular Difference Kernel

After reviewing the literature, I could not find an analytic solution to the equation $$\int^{1}_{0}dx\frac{f(x)}{|x-y|^{2/3}}=cf(y)$$ for $f(y)$, where $c$ is a constant and $y\in[0,1]$. I'm ...
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0answers
117 views

Solving Burger's equation and continuity with a pressure forcing term for a gas [closed]

I'm trying to solve this Burger's equation and continuity with a pressure forcing term. Below is the code snippet that I've tried already for the non-dimensionalized equations. The parameter ...
2
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0answers
126 views

Integral on unit disk of a function with two singularities

The goal is to prove, using Mathematica, that for $\mathbb{D}$ the unit disk and $u,v \in \mathbb{D}$, $u \neq v$, $$\frac{1}{\pi} \int_{\mathbb{D}} \frac{\mathrm{d}^2z}{(z-u)\overline{(z-v)}} = \ln(1-...
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2answers
214 views

Using NDSolve with Manipulate when singularity or stiffness detected

I want to solve a little bit complicated system of ODEs, where I have to vary initial conditions. My attempt to solution is like this (similar to what I found here Using ndsolve within manipulate): <...
2
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1answer
110 views

Nintegrate: How to define range of integration with moving singularities

I have to do an integral, like this NIntegrate[1/Sqrt[(Energy - ℏ ω)^2 - Δ^2], {Energy, Δ, Δ + ℏ ω}] How can I insert these singularities ...
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0answers
74 views

Variables defined modulo $\pi$ and avoiding singularities; phase plotting for a map

I have the following $2$-dimensional implicitly defined map ...
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1answer
117 views

Plotting numerically solved integration function with Logarithmic singularity

I am struggling to plot the following Numerically solved integral function. But my code is suffering from logarithmic singularity which it should not because xlnx is zero when x tends to zero. Any ...
2
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1answer
1k views

How to evade singularity or stiff system suspected in NDsolve?

I need to integrate my ODE between $t=10^{-29} s$ to $t=10^{-20} s$, so I did; ...
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0answers
59 views

Singular point problem [closed]

I have two functions: Uinf = 1; Λ = 30; ϕ[x_, y_] := Λ*Log[Sqrt[x^2 + y^2]]/(2*Pi) + Uinf*x; ψ[x_, y_] := Λ*ArcTan[y/x]/(2*Pi) + Uinf*y; I want to plot these ...
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0answers
32 views

Errors with NIntegrate: NIntegrate::ncvb and NIntegrate::slwcon

The image shows the array (W) I'm trying to integrate. It gives the following errors: 1. NIntegrate::ncvb 2. NIntegrate::slwcon I tried excluding the singularity points; adjusting the accuracy goal, ...
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1answer
79 views

NIntegrate complaining of not converging at a point outside the range

I am trying to evaluate the following numerical integral with mathematica but it is complaining of failing to converge around points outside the range. ...
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0answers
100 views

Problem with Singularity/Stiff

I need solve this equation, but i have problems with singularity/stiff ...
0
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2answers
188 views

Is there a way to specify the singularities of this integrand in order to numerically integrate it?

I have a function defined in terms of an integral which I need: fun[y2_]:=Integrate[x^2*Log[1 - Exp[-Sqrt[x^2 + y2]]], {x, 0, \[Infinity]} ] Unfortunately there ...
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0answers
79 views
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1answer
62 views

How to evaluate the integral and find values

I have following the following integral, $$\int_{-1}^{1} \sqrt{(1-a+0.5(1+2b))\left(\frac{1}{r^{6}-1+i 0^{+}}- (a+2b)\right)}dr= \Pi$$ I want to draw a plot of how $b$ vary when $a$ varies from $0.5$...
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62 views

How to specify this function in mathematica and take integral?

I have this function, $$F(r) = \frac{1}{r^{6}-1+i 0^{+}}$$ I don't know how to specify a function like this in Mathematica. The problem is how to specify the infinitesimal small imaginary part. ...
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0answers
93 views

ODE with singularity at origin and boundary condition at $\infty$ [duplicate]

I'm trying to solve the following ordinary differential equation numerically. ...
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0answers
249 views

Another NDSOLVE::ndsz: … singularity of stiff system suspected

I would be very grateful for any help with my "NDSOLVE::ndsz : At t==0.364197...., step size is effectively zero; singularity of stiff system suspected" error. Below is my code. I am not free to ...
3
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4answers
288 views

Patching removable singularities of a function

How can I make FunctionDomain include removable singularities? For instance, FunctionDomain[Sinc[x], x] == True But ...
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1answer
84 views

Integrate returns function which wrongly contains singularities at certain parameters

I am trying to generate a function that represents essentially a Beta Distribution that revolved around the Y axis. To do this I am trying to integrate only one quadrant because the expansion from ...
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1answer
106 views

Analytical definite integral yields wrong result [duplicate]

I'm trying to perform an analytical definite integral. 2/c*(Integrate[(r^2 + (M*a)^2)/( r^2 - 2*M*r + (M*a)^2), {r, rp + del, rmax}]) Here are all the parameters:...
5
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2answers
418 views

Plot gives 1/0 on singularity of elementary function [duplicate]

My understanding is that Mathematica 11 Plot can now handle singularities automatically when plotting. identify-types-of-singularities-and-discontinuitie I found ...
0
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2answers
156 views

NIntegrate versus Newton-Cotes or Gauss quadrature or other quadrature rules

I am trying to integrate the following function, f(r)=(80.50305990274495 - 35.03089630981622 r)/(80.50305990274495 - 79.5030598897815 r - r^2) where r =[0,1] ...
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1answer
112 views

NIntegrate for integrant with an obvious singularity

I know there are lots of posts like this one, but there is no hope for me to adopt any other experiences since the task seems to be very specific, at least from my level of understanding. I have to ...
2
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1answer
196 views

Numerical solution of singular non-linear integral equation

I want to extend this collocation method based mathematica scheme to solve following non-linear integral equation (Cauchy/Carleman type): $$B(v)/(1-v) \int_{0}^{1} \mathrm{d}x B(x) (1-x)/(v-x) = 1 $$ ...
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0answers
53 views

How do I get the output of a square-wave input? (singularity problem)

I am trying to get the electrical response of a system to an input square wave. Here is the code: ...
10
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1answer
320 views

Fourier transform inconsistency

Bug introduced in 5 or earlier and persisting through 11.3.0 On Mathematica 11.0.0 the Fourier transform of $x\theta(x)$ gives the expected result: ...