stable gravity integration?

[realMakc]

I tried smth like:

a = -r^-2;
v += a * dt;
x += v * dt;

but, major problem with this is when particles go close to each other they gain a LOT of speed.

I tried constrain acceleration like:

a = -Math.max (const, r)^-2

But this does not help much. I was thinking about advanced integration like RK etc, but does it really help in this situation? Anyone with experience in this please comment.