Questions on the use of numerical functions NIntegrate and NDSolve.
15
votes
2answers
618 views
Why does Mathematica give the wrong answer when integrating?
I integrate
Integrate[Exp[I Cos[b - c]] Cos[b], {b, 0, 2 Pi}]
Mathematica gives:
2 I Pi BesselJ[1, 1]
Which is indepedent ...
7
votes
4answers
332 views
4
votes
2answers
806 views
PDE Boundary Conditions
I am solving a PDE using Mathematica and I would like to know how to implement the condition that the two-variable function y[t,s] is zero whenever ...
7
votes
5answers
311 views
How to distinguish between lists and values?
I have a (hopefully small) problem with some numerical integration algorithm, more specifically I want to integrate the imaginary part of a complex valued function, e.g. ...
4
votes
2answers
389 views
How to solve for an Z-Score of a T-Distribution?
I'm looking for the Z-Score for a distribution, where the integrated area sums up to 0.90. Unfortunately I always get an error from Mathematica, ...
3
votes
2answers
410 views
Compute integral symbolically or numerically
I want to compute the integral of the following integrand
...
4
votes
0answers
222 views
Increase precision of custom function
I hope the title is not misleading:
Suppose I have a function that is quite complicated, e.g.
f[u_] := Exp[-Exp[- Abs[c.u]^a] Sin[d.u] Sin[(Abs[c.u]^a) ...
I ...
8
votes
1answer
885 views
Kramers-Kronig in Mathematica
I am trying to calculate the change of the refractive index from the change of the absorption coefficient using the Kramers-Kronig relations, in Mathematica.
...
12
votes
4answers
1k views
Numerical Fourier transform of a complicated function
Say I have a function $f(x)$ that is given explicitly in its functional form, and I want to find its Fourier transform[1]. If $f$ is too complicated to have an analytic expression for $\hat f(k)$, how ...
11
votes
1answer
934 views
Parallelizing Numerical Integration in Mathematica
I have an ugly, six dimensional function that I need to integrate numerically. It works, but it currently take twelve hours to complete the calculation. Is there any good way to parallelize the ...
7
votes
2answers
306 views
How to apply restrictions to the “integrated” variable, when using NDSolve?
I have to integrate an energy along a path. I know the energy at the "beginning" of the path (energy[0]), and I can determine the energy change (gain and loss) ...
21
votes
4answers
548 views
How to use NDSolve to track equilibrium?
I am looking for an extension of NDSolve where integration runs until certain variables are settled at an equilibrium. Now I have a working solution in my sleeves ...
12
votes
1answer
327 views
How to guarantee that NDSolve correctly detects abrupt changes in parameters?
When using NDSolve, I often have parameters that, in most of their domain, have a constant or null variation, but that suffer from abrupt variations on a very small ...
17
votes
1answer
252 views
Is there an NDSolve`ProcessEquations analog for NIntegrate?
NDSolve has an interface for repeatedly solving an equation with different initial conditions without having to analyze the equation and set up the solving algorithm each time. This can improve ...
