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9
votes
0answers
345 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 ...
5
votes
2answers
223 views
4
votes
2answers
650 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 ...
3
votes
1answer
648 views

Singular integral: NIntegrate fails to converge

I need to calculate the following singular integral: NIntegrate[Log[1 + y^2]/Cos[Pi y], {y, 0, 1}] However, it is failing to converge. I have tried to specify ...
3
votes
1answer
472 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\ ...
3
votes
0answers
170 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 ...
2
votes
1answer
167 views

Singularity on a simple Plot

While solving quartic equation ...
2
votes
2answers
617 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
110 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 ...
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
412 views

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

I am doing an Numerical integral with sigularities. ...
0
votes
1answer
89 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
130 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
26 views

ParametricNDSolve of differential equation with singularity

I have a differential equation I would like to solve with the ParametricNDSolve. However, the coefficients in the differential equation are singular at a certain value, so sometimes NDSolve crashes ...
0
votes
0answers
26 views

Taking limit of a singular function does not answer

I'm trying to take limit of a function like this that is singular in d=3 ("Infinite expression 1/0. encountered"). Do you know how it is possible take this limit? Plotting the function is ...
0
votes
0answers
82 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
103 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. I have attached the code defining the ...