# Questions tagged [singularity]

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

82 questions
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### 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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### 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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### 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 ...
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### 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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### 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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### Handing singularity of numerical integral to high precision

Consider the integral ...
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### 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): <...
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### 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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### 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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### 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 ...
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### 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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### 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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### 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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### 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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### Problem with Singularity/Stiff

I need solve this equation, but i have problems with singularity/stiff ...
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### 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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### Mathematica can't evaluate the function at the point where it is smooth

Suppose the function ...
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### 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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### 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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### 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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### 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 ...
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### 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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### 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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### 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:...
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### 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 ...
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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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### 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 ...
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### 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): $$B(v)/(1-v) \int_{0}^{1} \mathrm{d}x B(x) (1-x)/(v-x) = 1$$ ...
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: ...