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Evaluate a method to eliminate energy drift in explicit numerical integration of celestial dynamical systems.

August 12, 2026Open Access

Eliminating Energy Drift in Explicit Integration via Post-Step Velocity Rescaling: A 26-Year Mercury Orbit Benchmark

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Technical note evaluates post-step velocity rescaling's effectiveness in eliminating energy drift in celestial simulations.

Evaluate a method to eliminate energy drift in explicit numerical integration of celestial dynamical systems.
Implemented post-step velocity rescaling on standard 4th-order Runge-Kutta (RK4) method.
Constrained state vector to target energy surface at each integration step.
Conducted simulation over 26 years with a step size of 3600 seconds.
Achieved zero energy drift (delta_a = 0.00 m) over 26 years compared to 70.4 m drift with standard RK4.
Demonstrated efficacy in stabilizing orbital semi-major axis without step-size reduction.
Provided a lightweight correction layer for explicit numerical solvers.

Maksym Koresh (2026) studied this question.

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