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12
votes
1answer
171 views

Why do singularities disappear when performing convolutions with the Dirac Delta function?

I am attempting to perform a convolution involving the Dirac Delta function: $\int_{-\infty}^{\infty} \frac{1}{t+1} \cdot \delta(t+1)\ dt$ I would expect that the result of this integral is ...
10
votes
0answers
452 views

How does Mathematica find a series expansion of expressions containing logarithms when there is a singularity at the expansion point?

I am looking for a good approximation to a function containing logarithms, especially at values close to zero. When I used Mathematica's Series command I found ...
7
votes
2answers
239 views

Extending NDSolve beyond a singularity

The $\tan$ function satisfies the following IVP: $$y'=1+y^2 ,\quad y(0)=0 $$ and has simple poles at the points $x=\pi/2+ \pi n$ for integer $n$. When trying to get $\tan$ via numerical integration,...
7
votes
2answers
271 views

NIntegrate fails to converge under almost any PrecisionGoal, MinRecursion etc. How can I trust the result?

I have been getting some ideas by reading other related questions in the forum, but the integral I have to do is not converging in many cases. The integrand is of the form: ...
5
votes
2answers
896 views
4
votes
2answers
808 views

What can I do to eliminate the error FindFit::nrjnum:?

I am testing the "Power Law with finite-time singularity" hypothesis for world population growth for a project. The data I'm using (same behaviour should also be exhibited by the stock market, thats ...
4
votes
1answer
573 views

Multi-dimensional integral in the complex plane with poles and essential singularity

I've passed the last week searching a way to numerically integrate this multi-dimensional integral in the complex plane at the poles and avoiding the singularity at z=0: $$ \oint_{C}\oint_{C\ auound\ ...
4
votes
0answers
75 views

Why does Mathematica gives a solution which is not in the domain of the cot function? [closed]

I've tried to solve the equation $\cot \theta = 2 \cot 2\theta$ with the command Reduce and Mathematica gave $\theta = n\pi$ as solution, with $n$ an integer. But $\...
3
votes
1answer
76 views

In NMinimize, how can I efficiently handle NIntegrate errors for non-integrable functions?

I am using NMinimize to find parameters that minimise the integral of a function in the least squares sense: ...
3
votes
1answer
204 views

NIntegrate and Integrate giving different results for ill-behaved function

I'm trying to integrate the following function with Mathematica 8: $$ I(a,b)= \int_0^1 \mathrm{d}x\int_0^1\mathrm{d}y \,\theta(1-x-y) \frac{1}{x a^2-y(1-y)b^2},$$ where $\theta$ is the Heaviside ...
3
votes
0answers
56 views

Singularity treatment in a simple problem [duplicate]

With a simple search, several posts can be found on treating singularities encountered while using NDSolvefamily of numerical methods. However, most of them involve ...
3
votes
0answers
233 views

How to do Fast Fourier transform (FFT) for singular functions?

I want to do a 3-dimensional FFT on this function $\frac{\cos (x) \cos (y) \cos (z)-\sin (x) \sin (y) \sin (z)}{\left((1.0001+\sin (y)+\cos (z))^2+(0.0001+\cos (x)+\sin (z))^2+(0.0001+\sin (x)+\cos (y)...
2
votes
1answer
242 views

Singularity on a simple Plot

While solving quartic equation ...
2
votes
1answer
907 views

NIntegrate(with singularities) gives different results, which one should I trust?

I am doing an Numerical integral with sigularities. ...
2
votes
2answers
863 views

How to remove a singularity with WhenEvent

Bellow I have a differential equation which hits a singularity at low values of t. What I want to do is somehow utilize the WhenEvent command in order to replace ...
2
votes
1answer
62 views

How to properly plot with DensityPlot the singularities in a non-trivial phase profile of a function?

Consider as an example the following function: ...
1
vote
1answer
1k views

How to find local minima of a multivariate function with singularity?

I am working on a logistic regression problem which requires minimizing a cost function J[{theta0, theta1, theta2}, X, y] to find the optimal value for fitting ...
1
vote
1answer
91 views

To deal with infinity in NDSolve

I just started to learn to use Mathematica, and was trying to obtain an inverse function. Helpful comments lead to the use of NDSolve, but I encountered the problem ...
1
vote
1answer
172 views

Plotting singular integral

I need to plot the following singular double integration $u(x,t)$ for $t=0, t=0.2, t=0.4, t=1$ and $t=2$ in one figure as a line. That is, I need $u$-coordinate vertically and $x$-coordinate ...
1
vote
1answer
83 views

Is it possible to avoid the singularity problem of a 2nd order differential equations by restricting the solution range?

I would greatly appreciate your help in implementation of Mathematica for solving a 2nd order differential equation expressing some important engineering problem. Apparently, this equation has no ...
1
vote
1answer
107 views

Singularity problem of a 2nd order differential equation

I would greatly appreciate your help in implementation of Mathematica for solving a 2nd order differential equation expressing some important engineering problem. Apparently, this equation has no ...
1
vote
0answers
41 views

Behavior of solution to a ODE near a singular point [closed]

I want to see how the solution to the following ODE looks near z=z0. ...
0
votes
1answer
119 views

Solving ODE system with NDSolve: “singularity or stiff system suspected” [closed]

I'm trying to solve a set of 4 ODEs as specified below, however I'm getting this error ...
0
votes
1answer
122 views

How to compute DSolve or NDSolve for kind of piece wise function?

I need to Compute the expression for two functions. q[t] and q1[t] over certain range of time. The code is given below. ...
0
votes
1answer
162 views

Multiple NIntegral with singularity

I need to compute the following integral FF[0]. When evaluating FF[0] Mathematica simply takes too much time. The problem may ...
0
votes
0answers
69 views

Help numerically solve this non-linear PDE with singularity

I have trouble finding a numerical solution to the partial differential equation below. It seems to be a singularity in the solution somewhere, so I searched online and found that it is suggested to ...
0
votes
0answers
101 views

solving singular matrix [duplicate]

Hello I have a matrix that is singular, and i wanted to use linear solve to solve it but that doesn't work with mathematica. The matrix given as a list looks like this: ...
0
votes
0answers
193 views

Boundary value problem: complicated functionals

I am trying to solve a non-linear boundary value problem where the differential equation is a convoluted function of the variable I am trying to solve for. The equation below presents the final form ...