# [SciPy-user] Suggestions for Integro-Differential Equations

Lorenzo Isella lorenzo.isella@gmail....
Sun Apr 8 20:47:42 CDT 2007

Dear All,
I would like to solve numerically the following equation (I use
latex-style notation) [for those who are interested, this is
Smoluchowski equation describing the coagulation of aerosol particles]:

\frac{dn(v,t)}{dt}=\frac{1}{2}\int_{v_0}^{v-v_0}
K(v-q,q)n(v-q,t)n(q,t)dq-n(v,t)\int_{v_0}^\infty K(q,v)n(q,t)dq,
where K(q,v) is the appropriate collision kernel and n is a particle
concentration.
I am not familiar with integro-differential equations (which could be
the real problem) and I'll add that the equation above can be expressed
also in a discrete form, which is supposed to be even worse to be dealt
with numerically and that I am thus leaving out.
Any suggestions about how to deal with the equation above in Python? I
wonder if there is some tool for this sort of problems.
Cheers

Lorenzo