Class VerletIntegrator

java.lang.Object

org.episteme.core.mathematics.analysis.ode.VerletIntegrator

public class VerletIntegrator
extends Object

Verlet integration for molecular dynamics and N-body simulations.

Symplectic integrator: conserves energy over long simulations. Better for Hamiltonian systems than Runge-Kutta.

*

Reference:
Verlet, L. (1967). Computer 'experiments' on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Physical Review, 159(1), 98.

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Constructor Summary

Constructors

Constructor	Description
VerletIntegrator()

Method Summary

Modifier and Type	Method	Description
static Real[][]	integrate(Real[] x0, Real[] v0, Function<Real[],Real[]> acceleration, Real dt, int steps)	Integrate using arbitrary precision Real numbers over multiple steps.
static Real[][]	step(Real[] positions, Real[] velocities, Function<Real[],Real[]> acceleration, Real dt)	Velocity Verlet integration step using arbitrary precision Real numbers.

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

VerletIntegrator

public VerletIntegrator()

Method Details

integrate

public static Real[][] integrate(Real[] x0,
 Real[] v0,
 Function<Real[],Real[]> acceleration,
 Real dt,
 int steps)

Integrate using arbitrary precision Real numbers over multiple steps.

Parameters:

x0 - Initial positions

v0 - Initial velocities

acceleration - Acceleration function

dt - Time step

steps - Number of steps

Returns:

Final [positions, velocities]

step

public static Real[][] step(Real[] positions,
 Real[] velocities,
 Function<Real[],Real[]> acceleration,
 Real dt)

Velocity Verlet integration step using arbitrary precision Real numbers.

Parameters:

positions - Current positions x[n]

velocities - Current velocities v[n]

acceleration - Function computing acceleration from positions

dt - Time step

Returns:

Updated [positions, velocities] after one step