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2

A first step, if you "have never been up in computing", is to read the literature and see what others are doing and have done. The second step is that you will likely learn that what you want to do is not possible today -- at least unless you have access to supercomputers. I suspect that 3 billion particles is possible today, but only if you have access to ...


26

There are a few ways to conserve energy during ODE integration. Method 1: Symplectic Integration The cheapest way that is to use a symplectic integrator. A symplectic integrator solves the ODE on a symplectic manifold if it comes from one, and so if the system comes from a Hamlitonian system, then it will solve on some perturbed Hamiltonian trajectory. ...


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I see at least one important problem. On the right hand side you have a term that looks like $$P_o \left( \frac{\dot{R}}{R} \right)^{3 \kappa}$$ This term is dimensionally inconsistent with the other terms in the brackets, which have dimensions of a pressure. This term should actually be $$P_o \left( \frac{R_o}{R} \right)^{3 \kappa}$$ The paper you link ...


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