Best ODE algorithm to use for time/velocity independent potentials?

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SUMMARY

The discussion focuses on selecting an optimal Ordinary Differential Equation (ODE) algorithm for simulating the motion of 150 to 300 points interacting through distance-dependent potentials, akin to Newton's law of gravitation. Participants recommend the Runge-Kutta method, specifically the fourth-order version (RK4), for its balance of accuracy and simplicity. The user currently employs the Beeman algorithm for energy conservation but seeks improved trajectory accuracy. Comparisons between RK4 and Beeman indicate that RK4 may enhance trajectory precision.

PREREQUISITES
  • Understanding of Ordinary Differential Equations (ODEs)
  • Familiarity with numerical methods for simulating physical systems
  • Knowledge of the Runge-Kutta method, particularly RK4
  • Experience with energy conservation techniques in simulations, such as the Beeman algorithm
NEXT STEPS
  • Research the implementation details of the Runge-Kutta 4th order method (RK4)
  • Explore the Beeman algorithm and its applications in energy conservation
  • Investigate the velocity-Verlet algorithm and its advantages for trajectory accuracy
  • Study error propagation in numerical simulations to understand its impact on accuracy
USEFUL FOR

Researchers, physicists, and computational scientists interested in simulating large systems of particles under distance-dependent potentials, particularly those focused on improving accuracy in trajectory calculations.

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Hello, I am not sure if this is the right place to ask this, but I don't readily see a "numerical methods" forum here so I assumed this would be the place to go. Sorry if I overlooked another place to post this!

Anyway, I have some points interacting via potentials that are dependent only on distances (IE, not time or velocity), and I am wondering what would be the best ODE algorithm to use to simulate the motions of these points. The number of interacting points is fairly large, from 150 to 300. Let's say they're interacting via an additive pairwise potential similar to Newton's law of gravitation.

What would be a decent ODE algorithm to use that is both fairly accurate (and not subject to huge error propagation) and not too complicated for solving the equations of motion?

Any help would be greatly appreciated.
 
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Runge-Kutta is a standard ODE algorithm for problems like yours. Try a fourth order for reasonably decent convergence.
 
Is RK4 noticeably better than, for example, Beeman or velocity-Verlet? I've never used RK4, though I know it's the word for many people. I don't know much about it. Right now, I'm using Beeman for energy conservation, though what I'm most interested in is accuracy of trajectories. Would RK give me a bump up in this category?

Thank you in advance!
 

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