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-1
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0answers
40 views

Numerical solution of an ODE with a singularity at the initial value

I have a differential equation: (c^2-y[x]^2)*y'[x] - (a+b)*y[x]^2 + ((2/x)*c^2)*y[x] - c^2*b = 0 with the initial condition ...
1
vote
1answer
54 views
0
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1answer
69 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
62 views

Convergence problems with numerical integration of specific functions

I want to numerically integrate two functions that have several poles inside the integration region. These are the functions: ...
8
votes
0answers
145 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 ...
2
votes
1answer
269 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\ ...
2
votes
2answers
304 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 ...
4
votes
2answers
399 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
359 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 ...
1
vote
1answer
556 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 ...