Re: [Help-gsl] Re:Question regarding integration

[Simpson, Kenneth]

Hi - if this an electromagnetic potential problem, I may be able to 
help. 

But the problem as stated is confusing.

I realize it's hard to do math in ascii - and it may be a pain explaining 
the problem in sufficient detail.

I'd be interested in original problem statement. 

For instance, what was the nonhomogenous term in the wave equation? 

And by wave equation, I presume it was dervived from Maxwell's equations.

What do 's' and 'tau' denote? 

Where are source and field points? 

Since most of the questions will mostly be related to physics, we should 
probably take the discussion offline. 

I don't know much about MC - although I have played with them.

-- Ken


Jigal A wrote:
> Sorry for the long delay....
>
> The integration is of an electromagnetic (potential) field (5D) of a point
> source.
>
> The numerator is proportional to the (5D) velocity vector of the source
> (v_3 = cosh(s), v_0 = sinh(s), v_4 = 1, v_1 = v_2 = 0)
>
> The denominator is 1/R^(3/2) (the 5D green-function of the wave equation)
> where
> R^2 = x^2 + y^2 + (z - cosh(s))^2 + (tau - s)^2 - (t - sinh(s))^2
>
> I need to integrate all the potential components, namely, the 3 non-zero
> components.
> The edges where R=0 are regularized separately by hand.
> So - basically, the integrals are well defined, and basically, smooth
> functions of s.
> The denominator is a somewhat involved function, and if it could be shared,
> then it would save
> a few cycles.
>
> As for Monte Carlo method, I never thought of using non-deterministic
> methods such as MC.
> I thought that since the integrand is smooth function, I need to pursue more
> "exact", or
> deterministic methods.
>
> What do you think?
> What about integrating this as an ODE? Is that considered numerically good?
> (in terms of accuracy, that is).
>
> Best regards,
> Jigal.