# Questions tagged [singularity]

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

82 questions
0answers
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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 ...
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 ...
1answer
96 views

1answer
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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 ...
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 $x=y$, ...
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 ...
1answer
65 views

### Handing singularity of numerical integral to high precision

Consider the integral ...
3answers
139 views

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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): <...
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 ...
0answers
74 views

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

I have the following $2$-dimensional implicitly defined map ...
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 ...
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; ...
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 ...
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, ...
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. ...
0answers
100 views

### Problem with Singularity/Stiff

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

### Mathematica can't evaluate the function at the point where it is smooth

Suppose the function ...
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 $0.5$...
0answers
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. ...
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. ...
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 ...
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 ...
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 ...
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:...
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 ...
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] ...
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 ...
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): $$B(v)/(1-v) \int_{0}^{1} \mathrm{d}x B(x) (1-x)/(v-x) = 1$$ ...
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: ...
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: ...