# Parallel computation of a system of differential equation

I need to solve a system of differential equations which contains, at minimum, ten

thousands of differential equations. Actually, I am trying to solve density matrix

equation. It's like something $\frac{\partial}{\partial t}\rho(t) = \frac{-I}{\hbar}(H(t)\rho(t) -\rho(t)H(t))$.

If the dimension of Hilbert space is $N$, then there is $N^2$ coupled differential equations.

I want to know if it is possible to solve this system of differential equations in parallel

in Mathematica? My cpu has six cores, so I guess I can get a six times speed up, if I solve

the equations in parallel.

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If you have to deal with such a high number of equations, I'd suggest Fortran or C. There was a similar question here: scicomp.stackexchange.com/questions/8855/… –  Gregory Rut Apr 29 at 11:52
From the form of your equation I do not see how the system should be coupled, ist seems like the solution is a simple integration of any matrix element. To the topic: In general mathematica is not the tool to go when it comes to computation speed and memory efficiency. –  Wizard Apr 29 at 13:46
@ Wizrd. I edited the equation. What program do you suggest for such a problem? –  yashar Apr 29 at 14:09